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B|B) here means P(B on 2nd|B on 1st) 3.25 In a standard deck, there are 52 cards. Twelve cards are face cards (F) and 40 cards are not face cards (N). Draw two cards, one at a time, without replacement. The tree diagram is labeled with all possible probabilities. 216 Chapter 3 | Probability Topics Figure 3.14 a. Find P... |
enn diagram is as follows: Figure 3.15 3.27 Suppose an experiment has outcomes black, white, red, orange, yellow, green, blue, and purple, where each outcome has an equal chance of occurring. Let event C = {green, blue, purple} and event P = {red, yellow, blue}. Then C AND P = {blue} and C OR P = {green, blue, purple, ... |
sum of the probabilities in PT is 0.50. The total of all probabilities displayed must be 1, representing 100 percent of the sample space. If a student is selected at random, find the following: a. b. c. d. e. the probability that the student belongs to a club. the probability that the student works part time. the prob... |
Diagram, describe the overlapping area using a complete sentence. In the Venn Diagram, describe the area in the rectangle but outside both the circle and the oval using a complete sentence. Solution 3.30 a. P(O) =.51 b. P(R) =.075 because an average of 7.5 percent of African Americans have the Rh– –factor. c. P(O AND ... |
Record the results in the Without Replacement column section of Table 3.15. After you record the pick, put both candies back. Do this a total of 24 times, also. Use the data from Table 3.15 to calculate the empirical probability questions. Leave your answers in unreduced fractional form. Do not multiply out any fracti... |
R2) P(R1 AND G2) P(G2|R1) P(no yellows) P(doubles) P(no doubles) Table 3.15 Empirical Probabilities Discussion Questions 1. Why are the With Replacement and Without Replacement probabilities different? 2. Convert P(no yellows) to decimal format for both Theoretical With Replacement and for Empirical With Replacement. R... |
A) 2. P(B|A) = P(B) 3. P(A AND B) = P(A)P(B) mutually exclusive two events are mutually exclusive if the probability that they both happen at the same time is zero; if events A and B are mutually exclusive, then P(A AND B) = 0 outcome a particular result of an experiment probability a number between zero and one, inclu... |
inclusive. 3.2 Independent and Mutually Exclusive Events Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If two events are not independent, then we say that they are dependent In sampling with replacement, each member of a population is replaced after ... |
http://cnx.org/content/col30309/1.8 P(A|B) = P(A), and P(B|A) = P(B). If A and B are mutually exclusive, P(A OR B) = P(A) + P(B) and P(A AND B) = 0. 3.3 Two Basic Rules of Probability The multiplication rule—P(A AND B) = P(A|B)P(B) The addition rule—P(A OR B) = P(A) + P(B) − P(A AND B) Chapter 3 | Probability Topics 2... |
(H). 3. Find P(N). 4. Find P(F). 5. Find P(C). Use the following information to answer the next six exercises. A jar of 150 jelly beans contains 22 red jelly beans, 38 yellow, 20 green, 28 purple, 26 blue, and the rest are orange. Let B = the event of getting a blue jelly bean Let G = the event of getting a green jelly... |
G = the event of landing on green. Let Y = the event of landing on yellow. 22. If you land on Y, you get the biggest prize. Find P(Y). 23. If you land on red, you don’t get a prize. What is P(R)? Use the following information to answer the next 10 exercises. On a baseball team, there are infielders and outfielders. So... |
answer the next two exercises. You are rolling a fair, six-sided number cube. Let E = the event that it lands on an even number. Let M = the event that it lands on a multiple of three. 38. What does P(E|M) mean in words? 39. What does P(E OR M) mean in words? 3.2 Independent and Mutually Exclusive Events 40. E and F a... |
Table 3.16 shows a random sample of musicians and how they learned to play their instruments. Gender Self-Taught Studied in School Private Instruction Total Female Male Total 12 19 31 Table 3.16 38 24 62 22 15 37 72 58 130 54. Find P(musician is a female). 55. Find P(musician is a male AND had private instruction). 56... |
Find the probability that person used the product 11 to 20 times a day. Product Use (times per day) African Americans Native Hawaiians Latinos Japanese Americans Whites TOTALS 1–10 11–20 21–30 31+ TOTALS Table 3.17 Product Use by Ethnicity 60. Suppose that one person from the study is randomly selected. Find the proba... |
hit. 3.2 Independent and Mutually Exclusive Events Use the following information to answer the next 12 exercises. The graph shown is based on more than 170,000 interviews that took place from January through December 2012. The sample consists of employed Americans 18 years of age or older. The Health Index Scores are ... |
b. Find P(B). c. Find P(C|A). d. Find P(B|C). e. f. g. Find P(C AND B). h. i. Find P(C OR B). j. Are C and B mutually exclusive events? Show why or why not. In words, what is C|A? In words, what is B|C? In words, what is C AND B? 81. After a mayor of a major Canadian city announced his plans to cut budget costs in lat... |
This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 3 | Probability Topics 235 83. Compute the probabilities. a. P(you will get a chicken breast) b. P(you will get a 17-oz. chicken breast) c. P(you will get a chicken breast or you will not get a 17-oz. pork chop) d. P(you will not g... |
your answer in one to three complete sentences, including In words, explain what P(A|B) represents. Find P(A|B). numerical justification. f. Are A and B independent events? Explain your answer in one to three complete sentences, including numerical justification. 87. A special deck of cards has 10 cards. Four are gree... |
Find P(C OR D). e. Find P(D|C). 91. Y and Z are independent events. a. Rewrite the basic Addition Rule P(Y OR Z) = P(Y) + P(Z) - P(Y AND Z) using the information that Y and Z are independent events. b. Use the rewritten rule to find P(Z) if P(Y OR Z) =.71 and P(Y) =.42. 92. G and H are mutually exclusive events. P(G) ... |
95. Three professors at George Washington University did an experiment to determine if economists are more likely to return found money than other people. They dropped 64 stamped, addressed envelopes with $10 cash in different classrooms on the George Washington campus. Forty-four percent were returned overall. From t... |
to any person with any bloodtype. Their data show that 43 percent of people have type O blood and 15 percent of people have Rh– factor; 52 percent of people have type O or Rh– factor. a. Find the probability that a person has both type O blood and the Rh– factor. b. Find the probability that a person does not have bot... |
randomly selected senator would be up for reelection in November 2016? 103. What is the probability that a randomly selected senator was a Democrat and was up for reelection in November 2016? 104. What is the probability that a randomly selected senator was a Republican or was up for reelection in November 2014? 105. ... |
215 15 20 a. Complete the table. b. What is the probability that a randomly selected child will have wavy hair? c. What is the probability that a randomly selected child will have either brown or blond hair? d. What is the probability that a randomly selected child will have wavy brown hair? e. What is the probability... |
cookie and eats it. How many cookies did he take? a. Draw the tree that represents the possibilities for the cookie selections. Write the probabilities along each branch of the tree. b. Are the probabilities for the flavor of the second cookie that Miguel selects independent of his first selection? Explain. c. For eac... |
118. Given events G and H: P(G) =.43; P(H) =.26; P(H AND G) =.14 a. Find P(H OR G). b. Find the probability of the complement of event (H AND G). c. Find the probability of the complement of event (H OR G). 119. Given events J and K: P(J) =.18; P(K) =.37; P(J OR K) =.45 a. Find P(J AND K). b. Find the probability of t... |
age 65 or over|driver is female). d. Find P(driver is age 65 or over AND female). e. f. Find P(driver is age 65 or over). g. Are being age 65 or over and being female mutually exclusive events? How do you know? In words, explain the difference between the probabilities in Part c and Part d. 123. Suppose that 10,000 U.... |
with risk factors of becoming ill with the disease labeled as Methods A, B, and C and Other: Method A Method B Method C Other Totals Female 0 Male 2,146 Totals ____ Table 3.26 70 463 ____ 136 60 ____ 49 135 ____ ____ ____ ____ Suppose a person with a disease in Santa Clara County is randomly selected. a. Find P(Person... |
3 Two Basic Rules of Probability Baseball Almanac. (2013). Retrieved from www.baseball-almanac.com DiCamillo, Mark, and Field, M. The file poll. Field Research Corporation. Retrieved from http://www.field.com/ fieldpollonline/subscribers/Rls2443.pdf Field Research Corporation. (n.d.). Retrieved from www.field.com/field... |
www.nejm.org/doi/full/10.1056/NEJMoa033250 Samuels, T. M. (2013). Strange facts about RH negative blood. eHow Health. Retrieved from http://www.ehow.com/ facts_5552003_strange-rh-negative-blood.html The Disaster Center Crime Pages. (n.d.). United States: Uniform crime report – state statistics from 1960–2011. Retrieved... |
(G) = 20 150 = 2 15 =.13 9 P(R) = 22 150 = 11 75 =.15 11 P(O) = 150 − 22 − 38 − 20 − 28 − 26 150 = 16 150 = 8 75 =.11 13 P(E) = 47 194 =.24 15 P(N) = 23 194 =.12 17 P(S) = 12 194 = 6 97 =.06 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 3 | Probability Topics 245 19 13 52 = 1 4... |
,065 100,450 62 To pick one person from the study who is Japanese American AND uses the product 21 to 30 times a day means that the person has to meet both criteria: both Japanese American and uses the product 21 to 30 times a day. The sample space 4,715 100,450 should include everyone in the study. The probability is.... |
P(G AND E) does not equal 0. 87 NOTE The coin toss is independent of the card picked first. a. {(G,H) (G,T) (B,H) (B,T) (R,H) (R,T)} b. P(A) = P(blue)P(head) = ⎛ ⎝ ⎞ ⎠ 3 10 ⎞ ⎠ ⎛ ⎝ 1 2 = 3 20 c. Yes, A and B are mutually exclusive because they cannot happen at the same time; you cannot pick a card that is both blue an... |
) = P(type O) + P(Rh–) – P(type O AND Rh–) 0.52 = 0.43 + 0.15 – P(type O AND Rh–); solve to find P(type O AND Rh–) =.06 6 percent of people have type O, Rh– blood b. P(NOT(type O AND Rh–)) = 1 – P(type O AND Rh–) = 1 –.06 =.94 94 percent of people do not have type O, Rh– blood 99 a. Let C = be the event that the cookie... |
+ P(YG) = 25 64 + 15 64 + 15 64 = 55 64 d. P(G|G) = 5 8 e. Yes, they are independent because the first card is placed back in the bag before the second card is drawn. The composition of cards in the bag remains the same from draw one to draw two. 122a. 250 Chapter 3 | Probability Topics <20 20–64 >64 Totals Female.024... |
Probability Topics 251 d. 0 e. f. 463 3059 136 196 g. Figure 3.25 252 Chapter 3 | Probability Topics This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 4 | Discrete Random Variables 253 4 | DISCRETE RANDOM VARIABLES Figure 4.1 You can use probability and discrete random variables t... |
be drawn. The sample space for the drawing is red, white, and blue. Then, x = 0,1. If the marble we draw is red, then x = 1; otherwise, x = 0. Example 2: Let X = the number of female children in a randomly selected family with only two kids. Here we are only interested in families with two kids, not families with one ... |
x Relative Frequency of x Table 4.1 a. Which value(s) of x occurred most frequently? b. If you tossed the coin 1,000 times, what values could x take on? Which value(s) of x do you think would occur most frequently? c. What does the relative frequency column sum to? This OpenStax book is available for free at http://cn... |
) = 1 50 Table 4.2 X takes on the values 0, 1, 2, 3, 4, 5. This is a discrete PDF because we can count the number of values of x and also because of the following two reasons: a. Each P(x) is between zero and one, therefore inclusive b. The sum of the probabilities is one, that is, 2 50 + 11 50 + 23 50 + 9 50 + 4 50 + ... |
the P(x) column is 0.01+0.04+0.15+0.80 = 1.00. 4.2 Jeremiah has basketball practice two days a week. 90 percent of the time, he attends both practices. Eight percent of the time, he attends one practice. Two percent of the time, he does not attend either practice. What is X and what values does it take on? 4.2 | Mean ... |
2.2.5.3 (0)(.2) = 0 (1)(.5) =.5 (2)(.3) =.6 Table 4.5 Expected Value Table This table is called an expected value table. The table helps you calculate the expected value or longterm average. Add the last column x * P(x) to get the expected value/mean of the random variable X. E(X) = μ = ∑ xP(x) = 0 +.5 +.6 = 1.1 The e... |
To find the variance σ 2 of a discrete probability distribution, find each deviation from its expected value, square it, multiply it by its probability, and add the products. To find the standard deviation σ of a probability distribution, simply take the square root of variance σ 2. The formulas are given as below. NO... |
�� = 0 1 P(x = 1) = 11 50 ⎛ (1) ⎝ 11 50 ⎞ ⎠ = 11 50 2 P(x = 2) = 23 50 ⎛ (2) ⎝ 23 50 ⎞ ⎠ = 46 50 3 P(x = 3) = 9 50 ⎛ (3) ⎝ 9 50 ⎞ ⎠ = 27 50 4 P(x = 4) = 4 50 ⎛ (4) ⎝ 4 50 ⎞ ⎠ = 16 50 5 P(x = 5) = 1 50 ⎛ (5) ⎝ 1 50 ⎞ ⎠ = 5 50 Table 4.6 We then add all the products in the third column to get the mean/expected value of X.... |
9 50 =.0046 =.1458 4 P(x = 4) = 4 50 ⎛ (4) ⎝ 4 50 ⎞ ⎠ = 16 50 (4 − 2.1)2 = 3.61 3.61 • 4 50 =.2888 5 P(x = 5) = 1 50 ⎛ (5) ⎝ 1 50 ⎞ ⎠ = 5 50 (5 − 2.1)2 = 8.41 8.41 • 1 50 =.1682 Table 4.7 We then add all the products in the 5th column to get the variance of X. σ 2 =.1764 +.2662 +.0046 +.1458 +.2888 +.1682 = 1.05 To ge... |
. That means your profit is $100,000. If your five numbers do not match in order, you will lose the game and lose your $2. That means your profit is -$2. Therefore, X takes on the values $100,000 and –$2. That is the second column x in the PDF table below. To win, you must get all five numbers correct, in order. The pr... |
98. Since –.99998 is about –1, you would, on average, expect to lose approximately $1 for each game you play. However, each time you play, you either lose $2 or profit $100,000. The $1 is the average or expected loss per game after playing this game over and over. 262 Chapter 4 | Discrete Random Variables 4.5 You are p... |
win anything. If you land on green, you win $10. Complete the following expected value table. –20 5 x P(x) Red Blue Green 10 Table 4.12 2 5 Generally for probability distributions, we use a calculator or a computer to calculate μ and σ to reduce rounding errors. For some probability distributions, there are shortcut f... |
of the more common discrete probability functions are binomial, geometric, hypergeometric, and Poisson. Most elementary courses do not cover the geometric, hypergeometric, and Poisson. Your instructor will let you know if he or she wishes to cover these distributions. A probability distribution function is a pattern. ... |
options. This is a binomial experiment since it meets all three characteristics. The number of trials n = 1. There are only two outcomes, guess correctly or guess wrong, of each trial. We can define guess correctly as a success. For a random This OpenStax book is available for free at http://cnx.org/content/col30309/1... |
balls. So, p = 5 10 and q = 1 − p = 1 − 5 10 = 5 10. However, p and q do not remain the same for the second trial. If the first ball selected is red, then the probability of getting the second ball red is 4 9 since there are only four red balls out of nine balls. But if the first ball selected is blue, then the probab... |
is independent. If you play the game 20 times, write the function that describes the probability that you win 15 of the 20 times. Here, if you define X as the number of wins, then X takes on the values 0, 1, 2, 3,..., 20. The probability of a success is p = 0.55. The probability of a failure is q =.45. The number of t... |
there is only a success or a ________, there are a fixed number of trials, and the probability of a success is.70 for each trial. Solution 4.11 a. failure b. If we are interested in the number of students who do their homework on time, then how do we define X? Solution 4.11 b. X = the number of statistics students who... |
to define the probability of a binomial distribution P(x). We can use the formula to find P(x ≤ 12). But the calculation is tedious and time consuming, and people usually use a graphing calculator, software, or binomial table to get the answer. Use a graphing calculator, you can get P(x ≤ 12) =.9738. The instruction o... |
the pdf (binompdf). If you want to find P(x > 12), use 1 − binomcdf(20,.41,12). The probability that at most 12 workers have a high school diploma but do not pursue any further education is.9738. The graph of X ~ B(20,.41) is as follows. The previous graph is called a probability distribution histogram. It is made of ... |
, 2, 3, 4, 5, 6, 7, 8 b. This is a binomial experiment since all three characteristics are met. Each page is a trial. Since we sample 100 pages, the number of trials is n = 100. For each page, there are two possible outcomes, features signature artists or does not feature signature artists. Since we are measuring the n... |
probability that more than 30 adults prefer saving c. Using the formulas, calculate the (i) mean and (ii) standard deviation of X. Example 4.14 The lifetime risk of developing a specific disease is about 1 in 78 (1.28 percent). Suppose we randomly sample 200 people. Let X = the number of people who will develop the di... |
(x = 5) > P(x = 6); it is more likely that five people will develop the disease than six. 4.14 During the 2013 regular basketball season, a player had the highest field goal completion rate in the league. This player scored with 61.3 percent of his shots. Suppose you choose a random sample of 80 shots made by this play... |
trials until a success is obtained. Recall that a Bernoulli trial is a binomial experiment with number of trials n = 1. In other words, you keep repeating what you are doing until the first success. Then you stop. For example, you throw a dart at a bull's-eye until you hit the bull's-eye. The first time you hit the bu... |
2, 3,... (could go on indefinitely). Since we are measuring the number of games you play until you lose, we define a success as losing a game and a failure as winning a game. The probability of a success p =.57 and the probability of a failure q = 1 – p = 1 – 0.57 = 0.43. Both p and q remain the same from game to game... |
report showing an accident caused by employee failure to follow instructions, then the probability could be written as p =.35. If we want to find how many reports, on average, the safety engineer would expect to look at until she finds a report showing an accident caused by employee failure to follow instructions, we ... |
Read this as X is a random variable with a geometric distribution. The parameter is p; p = the probability of a success for each trial. Example 4.19 Assume that the probability of a defective computer component is 0.02. Components are randomly selected. Find the probability that the first defect is caused by the seven... |
.8 Chapter 4 | Discrete Random Variables 275 Figure 4.2 The previous probability distribution histogram gives all the probabilities of X. The x-axis of each bar is the value of X = the number of computer components tested until the first defect is found, and the height of that bar is the probability of that value occur... |
28 ⎞ ⎛ ⎝ ⎠ 1.0128 − 1 ⎞ ⎠ = (78)(78 − 1) = 6,006 = 77.4984 ≈ 77 The number of people whom you would expect to ask until one says he or she has pancreatic cancer is 78. And you expect that to vary by about 77 people on average. 4.20 The literacy rate for a nation measures the proportion of people age 15 and over who can... |
= the number of gumdrops in the sample of 50. X takes on the values x = 0, 1, 2,..., 50. What is the probability statement written mathematically? This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 4 | Discrete Random Variables 277 Solution 4.21 P(x = 35) 4.21 A bag contains letter... |
without replacement? Solution 4.23 a. without b. What is the group of interest? Solution 4.23 b. the men 278 Chapter 4 | Discrete Random Variables c. How many are in the group of interest? Solution 4.23 c. 15 men d. How many are in the other group? Solution 4.23 d. 18 women e. Let X = ________ on the committee. What v... |
there are two men on the committee is about.45. The graph of X ~ H(6, 5, 4) is Figure 4.3 The y-axis contains the probability of X, where X = the number of men on the committee. You would expect m = 2.18 (about two) men on the committee. The formula for the mean is μ = nr r + b = (4)(6) 6 + 5 = 2.18. 4.24 An intramura... |
you to find P(x = 3). 4.25 The average number of fish caught in an hour is eight. Of interest is the number of fish caught in 15 minutes. The time interval of interest is 15 minutes. What is the average number of fish caught in 15 minutes? Example 4.26 A bank expects to receive six bad checks per day, on average. What... |
random variable with a Poisson distribution. The parameter is μ (or λ); μ (or λ) = the mean for the interval of interest. Example 4.28 Leah's answering machine receives about six telephone calls between 8 a.m. and 10 a.m. What is the probability that Leah receives more than one call in the next 15 minutes? Let X = the... |
the standard deviation? Solution 4.29 a. P(x = 160) = poissonpdf(147, 160) ≈.0180 b. P(x ≤ 160) = poissoncdf(147, 160) ≈.8666 c. Standard Deviation = σ = μ = 147 ≈ 12.1244 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 4 | Discrete Random Variables 283 4.29 According to a recen... |
4.31 On May 13, 2013, starting at 4:30 p.m., the probability of low seismic activity for the next 48 hours in Alaska was reported as about 1.02 percent. Use this information for the next 200 days to find the probability that there will be low seismic activity in 10 of the next 200 days. Use both the binomial and Poiss... |
not a diamond. 5. Put the card back and reshuffle. 6. Do this a total of 10 times. 7. Record the number of diamonds picked. 8. Let X = number of diamonds. Theoretically, X ~ B(_____,_____) Procedure for Simulation Repeat the experimental procedure using a programmable calculator. 1. Use the randInt function to generat... |
theoretical PDF chart based on the distribution in the Procedure section. x P(x 288 Chapter 4 | Discrete Random Variables x P(x) 9 10 Table 4.17 b. Calculate the following: a. μ = ____________ b. σ = ____________ c. Construct a histogram of the theoretical distribution. Figure 4.7 Using the Data NOTE RF = relative fre... |
to determine if a Tet gambling game fits a discrete distribution. • The student will demonstrate an understanding of long-term probabilities. Supplies • One “Lucky Dice” game or three regular dice • One programming calculator Procedure Round answers to relative frequency and probability problems to four decimal places... |
Random Variables 6. Construct a histogram of the theoretical distribution. Figure 4.9 Use the Data NOTE RF = relative frequency Use the data from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places. 1. P(x = 3) = ________ 2. P(0 < x < 3) = ________ 3. P(x ... |
trial (for example, trial one) does not affect the results of the following trials, and all trials are conducted under the same conditions. Under these circumstances the binomial RV X is defined as the number of successes in n trials. The notation is: X ~ B(n, p). The mean is μ = np and the standard deviation is σ = n... |
. Notation X ~ H(r, b, n), where r = the number of items in the group of interest, b = the number of items in the group not of interest, and n = the number of items chosen. mean a number that measures the central tendency; a common name for mean is average The term mean is a shortened form of arithmetic mean. By defini... |
) is not necessarily a numerical set; the domain may be expressed in words; for example, if X = hair color then the domain is {black, blond, gray, green, orange} • We can tell what specific value x the random variable X takes only after performing the experiment standard deviation of a probability distribution experime... |
for each trial In a geometric experiment, define the discrete random variable X as the number of independent trials until the first success. We say that X has a geometric distribution and write X ~ G(p) where p is the probability of success in a single trial. The mean of the geometric distribution X ~ G(p) is μ = 1 − ... |
and n = the size of the chosen sample. X = the number of items from the group of interest that are in the chosen sample, and X may take on the values x = 0, 1,..., up to the size of the group of interest. The minimum value for X may be larger than zero in some instances. n ≤ r + b The mean of X is given by the formula... |
Through observation, the baker has established a probability distribution. x P(x) 1 2 3 4.15.35.40.10 Table 4.21 6. Define the random variable X. 7. What is the probability the baker will sell more than one batch? P(x > 1) = ________ 8. What is the probability the baker will sell exactly one batch? P(x = 1) = ________... |
= 1.6 Table 4.23 x P(x) x*P(x) (x – μ)2P(x) 2 4 6 8 0.1 0.3 0.4 0.2 2(.1) =.2 (2–5.4)2(.1) = 1.156 4(.3) = 1.2 (4–5.4)2(.3) =.588 6(.4) = 2.4 (6–5.4)2(.4) =.144 8(.2) = 1.6 (8–5.4)2(.2) = 1.352 Table 4.24 This OpenStax book is available for free at http://cnx.org/content/col30309/1.8 Chapter 4 | Discrete Random Variab... |
= the number of years a student will study ballet with the teacher. 300 Chapter 4 | Discrete Random Variables • Let P(x) = the probability that a student will study ballet x years. 28. Complete Table 4.28 using the data provided. x P(x) x*P(x) 1 2 3 4 5 6 7.10.05.10.30.20.10 Table 4.28 29. In words, define the random ... |
What is the standard deviation (σ)? 43. What is the probability that at most five of the freshmen reply yes? 44. What is the probability that at least two of the freshmen reply yes? 4.4 Geometric Distribution (Optional) Use the following information to answer the next six exercises: Researchers collected data from 203... |
in the first hour? 61. What is the probability that the store will have fewer than 12 customers in the first two hours? 62. Which type of distribution can the Poisson model be used to approximate? When would you do this? Use the following information to answer the next six exercises: On average, eight teens in the Uni... |
is a fair coin and is equally likely to land on heads or tails. • • • If the card is a face card, and the coin lands on heads, you win $6. If the card is a face card, and the coin lands on tails, you win $2. If the card is not a face card, you lose $2, no matter what the coin shows. a. Find the expected value for this... |
The third company, a biotech firm, has a 10 percent chance of returning $6,000,000 profit, a 70 percent of no profit or loss, and a 20 percent chance of losing the million dollars. a. Construct a PDF for each investment. b. Find the expected value for each investment. c. Which is the safest investment? Why do you thin... |
Entertainment Headquarters, rents DVDs and video games. The probability distribution for DVD rentals per customer at this shop is given as follows. They also have a five-DVD limit per customer. x P(x) 0 1 2 3 4 5.35.25.20.10.05.05 Table 4.36 e. At which store is the expected number of DVDs rented per customer higher? ... |
, there are 250 prizes of $5, 50 prizes of $25, and 10 prizes of $100. Assuming that 10,000 tickets are to be issued and sold, what is a fair price to charge to break even? 4.3 Binomial Distribution (Optional) 82. According to a recent article the average number of babies born with significant hearing loss (deafness) i... |
~ _____(_____,_____) d. How many of the 12 students do we expect to attend the festivities? e. Find the probability that at most four students will attend. f. Find the probability that more than two students will attend. Use the following information to answer the next three exercises: The probability that a local hoc... |
on. c. Give the distribution of X. X ~ _____(_____,_____) d. On average, how many schools would you expect to offer such courses? e. Find the probability that at most 10 offer such courses. f. Is it more likely that 12 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a c... |
define the random variable X. four years of high school? Justify your answer numerically. f. Based upon numerical values, is it more likely that four or that five of the seniors participated in after-school sports all four years of high school? Justify your answer numerically. In words, define the random variable X. 9... |
profit. If two of the dice show the number or object bet (and the third die does not show it), the player gets back his or her $1 bet, plus $2 profit. If all three dice show the number or object bet, the player gets back his or her $1 bet, plus $3 profit. Let X = number of matches and Y = profit per game. In words, de... |
. In words, define the random variable X. a. b. List the values that X may take on. c. Give the distribution of X. X ~ _____(_____,_____) d. On average, how many dealerships would we expect her to have to call until she finds one that has the car? e. Find the probability that she must call at most four dealerships. f. ... |
more than once. In words, define the random variable X. a. b. List the values that X may take on. c. Give the distribution of X. X ~ _____(_____,_____) d. How many pages do you expect to advertise footwear on them? e. Is it probable that all 20 will advertise footwear on them? Why or why not? f. What is the probabilit... |
What is the probability that you must ask 10 people? d. Find the (i) mean and (ii) standard deviation of the distribution of X. 312 Chapter 4 | Discrete Random Variables 111. According to a recent poll, 75 percent of millennials (people born between 1981 and 1995) have a profile on a social networking site. Let X = th... |
take on. c. Give the distribution of X. X ~ _____(_____,_____) d. How many instructors do you expect on the committee who are not technically proficient? e. Find the probability that at least five on the committee are not technically proficient. f. Find the probability that at most three on the committee are not techn... |
is one of the busiest in the world with an average of 60 births per day. Let X = the number of births in an hour. a. Find the mean and standard deviation of X. b. Sketch a graph of the probability distribution of X. c. What is the probability that the maternity ward will deliver three babies in one hour? d. What is th... |
3 percent. Given a bag of 144 fortune cookies, we are interested in the number of cookies with an extra fortune. Two distributions may be used to solve this problem, but only use one distribution to solve the problem. In words, define the random variable X. a. b. List the values that X may take on. c. Give the distrib... |
distribution of X. X ~ _____(_____,_____) d. How many seniors are expected to have participated in after-school sports all four years of high school? e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numeri... |
Experiment) 130. Use a programmable calculator to simulate a binomial distribution. a. How would you use the randInt function to simulate the number of successes in five trials of an experiment with two outcomes, each of which has a.5 probability of occurring? b. Use the randInt function to simulate 10 observations of... |
.org/indicator/ EG.ELC.ACCS.ZS?order=wbapi_data_value_2009%20wbapi_data_value%20wbapi_data_value-first&sort=asc 4.4 Geometric Distribution (Optional) Central Intelligence Agency. (n.d.). The world factbook. Retrieved from https://www.cia.gov/library/publications/theworldfactbook/geos/af.html Pew Research Center. (n.d.)... |
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