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Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of µ, and o;? (b) Suppose n = 25 and p = 0.15. Can we safely approximate the p distribu- tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of µ; and o;?

Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of µ, and o;? (b) Suppose n = 25 and p = 0.15. Can we safely approximate the p distribu- tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of µ; and o;?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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S AND SAMPLING DISTRIBUTIONS 15. Airline Flights: No-Shows Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight? X- (b) Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation? P(255 < r); P(r < 255); P(r < 267); P(r = 255) (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? 16. General: Approximations We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions made for each approxima- tion. Give details and examples in your essay. How could you apply these statistical methods in your everyday life? on, you discuss 17. Statistical Literacy Under what conditions is it appropriate to use a normal distribution to approximate the p distribution? 18.| Statistical Literacy What is the formula for the standard error of the normal approximation to the p distribution? What is the mean of the p distribution? 19.| Statistical Literacy Is p an unbiased estimator for p when np > 5 and ng > 5? Recall that a statistic is an unbiased estimator of the corresponding parameter if the mean of the sampling distribution equals the parameter in question. te 20.| Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of u, and o;? (b) Suppose n = tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of u; and o;? 25 and p 0.15. Can we safely approximate the p distribu- || Basic Computation: p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 100 and p bution by a normal distribution? Why? Compute (b) Suppose n = tion by a normal distribution? Why or why not? 21. 0.23. Can we safely approximate the p distri- and Op. 20 and p = 0.23. Can we safely approximate the p distribu- PART II SUMMARY In this part, we studied sampling distributions. We also looked at the normal approximation to the binomial distribution. The Chapter Review has a summary of the specific topics of this part, as well as Important Words and Symbols. Part II Chapter Review Problems: 4, 7, 8, 9, 10, 15, 17, 21, 22, 23, 24, 25, 26. ngage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208
Transcribed Image Text:S AND SAMPLING DISTRIBUTIONS 15. Airline Flights: No-Shows Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats. (a) What is the probability that a person holding a reservation will show up for the flight? X- (b) Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation? P(255 < r); P(r < 255); P(r < 267); P(r = 255) (c) Use the normal approximation to the binomial distribution and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? 16. General: Approximations We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions made for each approxima- tion. Give details and examples in your essay. How could you apply these statistical methods in your everyday life? on, you discuss 17. Statistical Literacy Under what conditions is it appropriate to use a normal distribution to approximate the p distribution? 18.| Statistical Literacy What is the formula for the standard error of the normal approximation to the p distribution? What is the mean of the p distribution? 19.| Statistical Literacy Is p an unbiased estimator for p when np > 5 and ng > 5? Recall that a statistic is an unbiased estimator of the corresponding parameter if the mean of the sampling distribution equals the parameter in question. te 20.| Basic Computation: p Distribution Suppose we have a binomial experi- ment in which success is defined to be a particular quality or attribute that interests us. 33 and p = 0.21. Can we approximate the p distribution by (a) Suppose n = a normal distribution? Why? What are the values of u, and o;? (b) Suppose n = tion by a normal distribution? Why or why not? (c) Suppose n = 48 and p = 0.15. Can we approximate the p distribution by a normal distribution? Why? What are the values of u; and o;? 25 and p 0.15. Can we safely approximate the p distribu- || Basic Computation: p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 100 and p bution by a normal distribution? Why? Compute (b) Suppose n = tion by a normal distribution? Why or why not? 21. 0.23. Can we safely approximate the p distri- and Op. 20 and p = 0.23. Can we safely approximate the p distribu- PART II SUMMARY In this part, we studied sampling distributions. We also looked at the normal approximation to the binomial distribution. The Chapter Review has a summary of the specific topics of this part, as well as Important Words and Symbols. Part II Chapter Review Problems: 4, 7, 8, 9, 10, 15, 17, 21, 22, 23, 24, 25, 26. ngage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. WCN 02-200-208
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