(A) Find the mean and standard deviation of the sampling distribution of p. Describe the shape of the sampling distribution. (B) What is the probability that the sample proportion would be between 0.4 and 1.0? (C) What is the probability that less than 135 out of 300 households would prefer the new toothpaste package?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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1. Marketing research indicated that 40% of the households in a town preferred certain new toothpaste
package. To conduct a further study, a random sample of 300 households would be collected. Let p
denote the sample proportion of 300 households that would prefer the new toothpaste package.
(A) Find the mean and standard deviation of the sampling distribution of p. Describe the shape of
the sampling distribution.
(B) What is the probability that the sample proportion would be between 0.4 and 1.0?
(C) What is the probability that less than 135 out of 300 households would prefer the new toothpaste
package?
(D) How would the mean and standard deviation of the sampling distribution change respectively if
a random sample of 500 households would be selected instead?
Transcribed Image Text:1. Marketing research indicated that 40% of the households in a town preferred certain new toothpaste package. To conduct a further study, a random sample of 300 households would be collected. Let p denote the sample proportion of 300 households that would prefer the new toothpaste package. (A) Find the mean and standard deviation of the sampling distribution of p. Describe the shape of the sampling distribution. (B) What is the probability that the sample proportion would be between 0.4 and 1.0? (C) What is the probability that less than 135 out of 300 households would prefer the new toothpaste package? (D) How would the mean and standard deviation of the sampling distribution change respectively if a random sample of 500 households would be selected instead?
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