Statistics Chapter 4, 5, 6 Exam

55

(1 answer) Two balls are selected from a box containing 11 balls. The order of selection is not important. How many simple events are in the sample space?

216

(1 answer) Use the mn Rule to find the number of items in the following exercise. Three dice are tossed. How many simple events are in the sample space?

(a)= 0.97 (b)= 0.03

(2 answers) A smoke-detector system uses two devices, A and B. If smoke is present, the probability that it will be detected by device A is 0.94; by device B, 0.95; and by both devices, 0.92. (a) If smoke is present, find the probability that the smoke will be detected by device A or device B or both devices. (b) Find the probability that the smoke will not be detected.

(a)= 0.2266 (b)= 99.62

(2 answers) Allen Shoemaker derived a distribution of human body temperatures, which has a distinct mound-shape.† Suppose we assume that the temperatures of healthy humans is approximately normal with a mean of 98.6 degrees and a standard deviation of 0.8 degrees. (a) If a healthy person is selected at random, what is the probability that the person has a temperature above 99.2 degrees? (Round your answer to four decimal places.) (b) What is the 90th percentile for the body temperatures (in °) of healthy humans? (Round your answer to two decimal places.)

(a)= 0.5986 (b)= 0.1003 (c)= 0.0808

(3 answers) A normal random variable x has mean 𝜇 = 7 and standard deviation 𝜎 = 5. Find the probabilities associated with the following intervals. (Round your answers to four decimal places.) (a) 1.3 < x < 10 (b) x > 13.4 (c) x ≤ 0

both A and B= E4 A or B or both= E1, E2, E4 not B= E2, E3

(3 answers) A sample space consists of S = E1, E2, E3, E4. Consider the following events A and B. A = E2, E4 and B = E1, E4 List the simple events in each of the following. (Enter your answers as comma-separated lists.) both A and B A or B or both not B

(a)= 0.925 (b)= 0.390 (c)= 0.972

(3 answers) Find P(x ≤ k) for each of the following cases. (Round your answers to three decimal places.) (a) n = 20, p = 0.05, k = 2 (b) n = 15, p = 0.6, k = 8 (c) n = 10, p = 0.7, k = 9

P(B)= 0.45

(1 answer) A sample space consists of five simple events with P(E1) = P(E2) = 0.25, P(E3) = 0.2, and P(E4) = 2P(E5). Find the probability of the event B = {E2, E3}.

C= {2, 3, 4, 5, 6}

(1 answer) A single six-sided die is tossed. List the simple events in C. (Enter your answers as a comma-separated list. If C contains no simple events, enter NONE.) C: observe a number greater than 1

0.4444

(1 answer) Assume that the heights of American men are normally distributed with a mean of 69.9 inches and a standard deviation of 3.2 inches. What is the probability that a randomly selected man will be between 5'9" and 6'1" tall? (Round your answer to four decimal places.)

1.4 times

(1 answer) Find the expected value of x, the average number of times a customer visits the store.

continuous

(1 answer) Identify the random variable as either discrete or continuous. Height of the ocean's tide at a given location

discrete

(1 answer) Identify the random variable as either discrete or continuous. Number of overdue accounts in a department store at a particular time

15,120

(1 answer) In how many ways can you select five people from a group of nine if the order of selection is important?

0.55

(1 answer) Let x have a uniform distribution on the interval 0 to 10. Find the probability. P(2.9 < x < 8.4)

0.8347

(1 answer) Let x have an exponential distribution with 𝜆 = 0.3. Find the probability. (Round your answer to four decimal places.) P(x < 6)

0.0498

(1 answer) Let x have an exponential distribution with 𝜆 = 1. Find the probability. (Round your answer to four decimal places.) P(x > 3)

0.84

(1 answer) Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Find the percentile. (Round your answer to two decimal places.) z0.20 or the 80th percentile

0.117

(1 answer) Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.) P(z > 1.19)

0.2485

(1 answer) Let z be a standard normal random variable with mean 𝜇 = 0 and standard deviation 𝜎 = 1. Use Table 3 in Appendix I to find the probability. (Round your answer to four decimal places.) between 0.55 and 1.72

(a)= 0.28 (b)= 0.36 (c)= 0.52

(3 answers) The thickness in microns (µ) of a protective coating applied to a conductor designed to work in corrosive conditions is uniformly distributed on the interval from 25 to 50. (a) What is the probability that the thickness of the coating is greater than 43 microns? (b) What is the probability that the thickness of the coating is between 34 and 43 microns? (c) What is the probability that the thickness of the coating is less than 38 microns?

(M, M, M), (M, M, F), (M, F, M), (M, F, F), (F, M, M), (F, M, F), (F, F, M), (F, F, F) 0.125 0.375

(3 answers) Three children are selected, and their gender recorded. Assume that males and females are equally likely. List the simple events in the sample space. (Enter your answer as a comma-separated list. Enter each simple event in the format (G1, G2, G3) where Gi is the gender of the ith child. Use M for male and F for female.) Each event is equally likely, with probability

a= 0.6 b= 0.15 c= 0.48 d= 0.03

(4 answers) (a) The adult is judged to need eyeglasses. (b) The adult needs eyeglasses for reading but does not use them. (c) The adult uses eyeglasses for reading whether he or she needs them or not. (d) An adult used glasses when they didn't need them.

(a)= 0.54 (b)= Yes, because the probability that the student orders a cafe mocha is 0.9 regardless of whether the student visits Starbucks or Peet's. (c)= 0.4 (d)= 0.96

(4 answers) A college student frequents one of two coffee houses on campus, choosing Starbucks 60% of the time and Peet's 40% of the time. Regardless of where she goes, she buys a cafe mocha on 90% of her visits. (a) The next time she goes into a coffee house on campus, what is the probability that she goes to Starbucks and orders a cafe mocha? (b) Are the two events in part (a) independent? Explain. (c) If she goes into a coffee house and orders a cafe mocha, what is the probability that she is at Peet's? (d) What is the probability that she goes to Starbucks or orders a cafe mocha or both?

(a)= 0.328 (b)= 0.410 (c)= 0.007

(4 answers) A new surgical procedure is said to be successful 80% of the time. Suppose the operation is performed five times and the results are assumed to be independent of one another. (Round your answers to three decimal places.) (a) What is the probability that all five operations are successful? (b) What is the probability that exactly four are successful? (c) What is the probability that less than two are successful?

P(A|C) ≠ P(A); are not P(A ∩ C) = 0; are

(4 answers) Are events A and C independent? Since __________, A and C ______ independent. Are events A and C mutually exclusive? Since_________, A and C ______ mutually exclusive.

(a)= 0.2212 (b)= 0.2231 (c)= 0.1447 (d)= 0.9502

(4 answers) The length of time of calls made to a support helpline follows an exponential distribution with an average duration of 20 minutes so that 𝜆 = 1/20 = 0.05. (Round your answer to four decimal places.) (a) What is the probability that a call to the helpline lasts less than 5 minutes? (b) What is the probability that a call to the helpline lasts more than 30 minutes? (c) What is the probability that a call lasts between 20 and 30 minutes? (d) Tchebysheff's Theorem says that the interval 20 ± 2(20) should contain at least 75% of the population. What is the actual probability that the call times lie in this interval?

(a)= 0.4 (b)= 𝜇=6 days and 𝜎=1.90 days (c)= 1.58

(4 answers) To check the accuracy of a particular weather forecaster, records were checked only for those days when the forecaster predicted rain "with 40% probability." A check of 15 of those days indicated that it rained on 9 of the 15. (a) If the forecaster is accurate, what is the appropriate value of p, the probability of rain on one of the 15 days? (b) What are the mean 𝜇 and standard deviation 𝜎 of x, the number of days on which it rained, assuming that the forecaster is accurate? (Round your standard deviation to two decimal places.) (c) Calculate the z-score for the observed value, x = 9. [HINT: Recall that z-score = (x − 𝜇)/𝜎.] (Round your answer to two decimal places.)

(a)= 0.9641 (b)= 0.3085 (c)= 0.9292 (d)= 0.3228

(4 answers) Using Table 3 in Appendix I, calculate the area under the standard normal curve to the left of the following. (Round your answers to four decimal places.) (a) z = 1.8 (b) z = −0.5 (c) z = 1.47 (d) z = −0.46

(a)= 0.13 (b)= 0.07 (c) mean= 1.99 and SD= 1.136 (d)= 0.99

(5 answers) (a) What is the probability that a randomly selected coffee drinker would take no coffee breaks during the day? (b) What is the probability that a randomly selected coffee drinker would take more than three coffee breaks during the day? (c) Calculate the mean and standard deviation for the random variable x. (Round your standard deviation to three decimal places.) (d) Find the probability that x falls into the interval 𝜇 ± 2𝜎.

(a) P(A) =0.48 (b) P(B) =0.82 (c) P(A ∩ B) =0.33 (d) P(A ∪ B) =0.97 (e) P(A|B) =0.402 (f) P(B|A) =0.688

(6 answers) (a) P(A) (b) P(B) (c) P(A ∩ B) (d) P(A ∪ B) (e) P(A|B) (f) P(B|A)

1. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team.

(question 17 continued) If less than two operations were successful, how would you feel about the performance of the surgical team? 1. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team. 2. It would be very unlikely for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would not lead one to question the skill of this surgical team. 3. It would be fairly common for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would not lead one to question the skill of this surgical team. 4. It would be fairly common for a team with a success rate of 80% to have fewer than two successful procedures out of five. Therefore, these results would lead one to question the skill of this surgical team.

p is accurate. 2. The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate.

(question 20 continued) (d) Do these data disagree with the forecast of a "40% probability of rain"? Explain. 1. The observed event is more than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate. 2. The observed event is less than 2 standard deviations above the mean, so it is not unlikely assuming p is accurate. 3. The observed event is less than 2 standard deviations above the mean, so it is very unlikely assuming p is accurate. 4. The observed event is more than 2 standard deviations above the mean, so it is unlikely assuming p is accurate.