Question 1 Find the following probabilities associated with the standard normal random variable z (Round to...
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Question 1 Find the following probabilities associated with the standard normal random variable z (Round to the four-decimal place only if your answer goes beyond the fourth decimal place) a. P(z>2.1)= [Select] b. P(Z < -1.2) = [Select] c. P(.5 <z<1.5) = [Select] d. P(-2.75 <z < -1.70) = = e. P(-1.96 < z < 1.96) = f. P(z > 1.645) = Question 2 [Select] [Select] [Select] Y Find the value of 20 such that the following probability statements are true: 0.6 pts 0.4 pts a. P(zzo) = .10; %0 = [Select] b. P(Z <zo) = .01; %0 = [Select] c. P(-20 < x < 20) = .95; 20: = d. P(zzo) = .2643; %0 = [Select] Question 3 If is normally distributed with mean 10 and variance 2.25, evaluate the following probabilities: P(z>8.5) b. P(x < 12) = a. [Select] [Select] [Select] c. P(9.25 < x < 11.25) = d. P(7.5 <2<9.2) = [Select] e. P(12.25 < x < 13.25) = Select] [ Select] 0.5 pts Question 4 Choose the proportions of the scores of a trade school entrance exam when it exhibits the characteristics of normal distribution with mean and standard deviation 50 and 5, respectively. a. What proportion of the scores on this examination would be greater than 60? b. What proportion of the scores on this examination would be less than 45? c. What proportion of the scores on this examination would be between 35 and 65? 0.9772, 0.1587, 0.9987 0.0228, 0.1587, 0.9974 0,9772, 0,8413, 0,0013 0.0228, 0.8413, 0.9987 0.9772, 0,8413, 0,9974 Question 5 0.3 pts a. At most 50% of white seeds? [Select] 1 pts A large number of seeds from a certain species of flower are collected and mixed together in the following proportions according to the color of the flowers they will produce: 2 red, 2 white, 1 blue. If these seeds are mixed and then randomly packaged in bags containing about 100 seeds, what is the probability that a bag will contain the following: b. At least 65 seeds that are not "white"? [Select] c. At least 25 but at most 45 "white" seed? [Select] d. Within what limits would you expect the number of white seeds to lie with probability .95? to [Select] from [Select] Question 6 An auditor has reviewed the financial records of a hardware store and has found that its billing errors follow a normal distribution with mean and standard deviation equal to $0 and $1, respectively. What proportion of the store?s billings is in error by more than $1? What is the probability that a billing represents an overcharge of at least $1,50? What is the probability that a customer has been undercharged from $.50 to $1.00? Within what range would 95% of the billing errors be? Of the extreme undercharges, 5% would be at least what amount? [Choose] [Choose] [Choose] [Choose ] 0.5 pts T [Choose] Question 7 Suppose is a binomial random variable with n = 400 and p = 0.1. Use the normal approximation to binomial probabilities to find following: a. P(X> 45)= = b. P(X ≤32) = [Select] c. P(34 ≤ x ≤ 46) = [Select] Question 8 0,9788 0.9719 Past records show that at a given college 20% of the students who began as psychology majors either changed their major or dropped out the school. An incoming class has 110 beginning psychology majors. What is the probability that as many as 30 of these students leave the psychology program? 0.9633 0.45 pts [Select] 0.6844 0.3 pts Question 9 The president of an agency specializing in public opinion surveys claims that approximately 70% of all people to whom the agency sends questionnaires responds by filling out an returning the questionnaire. Four such questionnaires are sent out. Let be the number of questionnaires that are filled out and returned. a. What is the probability that no questionnaires are filled out and returned? [Select] b. What is the probability that exactly three questionnaires are filled out and returned? [Select] c. What is the probability that at least three questionnaires are filled out and returned? Question 10 [Select] 0.45 pts b. Find the probability that at most one indicates that her next purchase will be either a compact or economy car. Probability= [Select] 0.4 pts A marketing research survey shows that approximately 80% of the car owners surveyed indicated that their next car purchase will be either a compact or economy car. Assume the 80% figure is correct and five prospective buyers are interviewed. a. Find the probability that all five indicate that their next car purchase will be either a compact or economy car. Probability = [Select] Question 11 The board of director of a company has voted to create an employee council for the purpose of handling employee complaints. The council will consist of the company president, the vice-president for personnel, and four employee representatives. The four employees will be randomly selected form a list of 15 volunteers. This list consists of nine men and six women. a. What is the probability that two or more men will be selected from the list of volunteers? [Select] b. What is the probability that exactly three women will be selected from the list of volunteers? Question 12 0,2810 0.6000 An auditor is checking the records of an accountant who is responsible for ten clients. The accounts of two of the clients contain major errors, and the accountant will fail the inspection if the auditor finds even a single erroneous account. What is the probability that the accountant will fail the inspection if the auditor inspects the records of three clients chosen at random? 0.3333 0.4 pts [Select] 0,5333 0.3 pts Question 13 Suppose it is known that 10% of the citizens of the United States are in favor of increased foreign aid. A random sample of 100 U.S. citizens is questioned on this issue. Find the mean and standard deviation of , the number of citizens who favor increased foreign aid. Mean = [Select] Standard Deviation = 0.4 pts [Select] Question 1 Find the following probabilities associated with the standard normal random variable z (Round to the four-decimal place only if your answer goes beyond the fourth decimal place) a. P(z>2.1)= [Select] b. P(Z < -1.2) = [Select] c. P(.5 <z<1.5) = [Select] d. P(-2.75 <z < -1.70) = = e. P(-1.96 < z < 1.96) = f. P(z > 1.645) = Question 2 [Select] [Select] [Select] Y Find the value of 20 such that the following probability statements are true: 0.6 pts 0.4 pts a. P(zzo) = .10; %0 = [Select] b. P(Z <zo) = .01; %0 = [Select] c. P(-20 < x < 20) = .95; 20: = d. P(zzo) = .2643; %0 = [Select] Question 3 If is normally distributed with mean 10 and variance 2.25, evaluate the following probabilities: P(z>8.5) b. P(x < 12) = a. [Select] [Select] [Select] c. P(9.25 < x < 11.25) = d. P(7.5 <2<9.2) = [Select] e. P(12.25 < x < 13.25) = Select] [ Select] 0.5 pts Question 4 Choose the proportions of the scores of a trade school entrance exam when it exhibits the characteristics of normal distribution with mean and standard deviation 50 and 5, respectively. a. What proportion of the scores on this examination would be greater than 60? b. What proportion of the scores on this examination would be less than 45? c. What proportion of the scores on this examination would be between 35 and 65? 0.9772, 0.1587, 0.9987 0.0228, 0.1587, 0.9974 0,9772, 0,8413, 0,0013 0.0228, 0.8413, 0.9987 0.9772, 0,8413, 0,9974 Question 5 0.3 pts a. At most 50% of white seeds? [Select] 1 pts A large number of seeds from a certain species of flower are collected and mixed together in the following proportions according to the color of the flowers they will produce: 2 red, 2 white, 1 blue. If these seeds are mixed and then randomly packaged in bags containing about 100 seeds, what is the probability that a bag will contain the following: b. At least 65 seeds that are not "white"? [Select] c. At least 25 but at most 45 "white" seed? [Select] d. Within what limits would you expect the number of white seeds to lie with probability .95? to [Select] from [Select] Question 6 An auditor has reviewed the financial records of a hardware store and has found that its billing errors follow a normal distribution with mean and standard deviation equal to $0 and $1, respectively. What proportion of the store?s billings is in error by more than $1? What is the probability that a billing represents an overcharge of at least $1,50? What is the probability that a customer has been undercharged from $.50 to $1.00? Within what range would 95% of the billing errors be? Of the extreme undercharges, 5% would be at least what amount? [Choose] [Choose] [Choose] [Choose ] 0.5 pts T [Choose] Question 7 Suppose is a binomial random variable with n = 400 and p = 0.1. Use the normal approximation to binomial probabilities to find following: a. P(X> 45)= = b. P(X ≤32) = [Select] c. P(34 ≤ x ≤ 46) = [Select] Question 8 0,9788 0.9719 Past records show that at a given college 20% of the students who began as psychology majors either changed their major or dropped out the school. An incoming class has 110 beginning psychology majors. What is the probability that as many as 30 of these students leave the psychology program? 0.9633 0.45 pts [Select] 0.6844 0.3 pts Question 9 The president of an agency specializing in public opinion surveys claims that approximately 70% of all people to whom the agency sends questionnaires responds by filling out an returning the questionnaire. Four such questionnaires are sent out. Let be the number of questionnaires that are filled out and returned. a. What is the probability that no questionnaires are filled out and returned? [Select] b. What is the probability that exactly three questionnaires are filled out and returned? [Select] c. What is the probability that at least three questionnaires are filled out and returned? Question 10 [Select] 0.45 pts b. Find the probability that at most one indicates that her next purchase will be either a compact or economy car. Probability= [Select] 0.4 pts A marketing research survey shows that approximately 80% of the car owners surveyed indicated that their next car purchase will be either a compact or economy car. Assume the 80% figure is correct and five prospective buyers are interviewed. a. Find the probability that all five indicate that their next car purchase will be either a compact or economy car. Probability = [Select] Question 11 The board of director of a company has voted to create an employee council for the purpose of handling employee complaints. The council will consist of the company president, the vice-president for personnel, and four employee representatives. The four employees will be randomly selected form a list of 15 volunteers. This list consists of nine men and six women. a. What is the probability that two or more men will be selected from the list of volunteers? [Select] b. What is the probability that exactly three women will be selected from the list of volunteers? Question 12 0,2810 0.6000 An auditor is checking the records of an accountant who is responsible for ten clients. The accounts of two of the clients contain major errors, and the accountant will fail the inspection if the auditor finds even a single erroneous account. What is the probability that the accountant will fail the inspection if the auditor inspects the records of three clients chosen at random? 0.3333 0.4 pts [Select] 0,5333 0.3 pts Question 13 Suppose it is known that 10% of the citizens of the United States are in favor of increased foreign aid. A random sample of 100 U.S. citizens is questioned on this issue. Find the mean and standard deviation of , the number of citizens who favor increased foreign aid. Mean = [Select] Standard Deviation = 0.4 pts [Select]
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Introduction To Probability And Statistics
ISBN: 9781133103752
14th Edition
Authors: William Mendenhall, Robert Beaver, Barbara Beaver
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