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Chapter 7: Q. 39 (page 441)

A sample survey interviews an SRS of 267college women. Suppose (as is roughly true) that 70%of college women have been on a diet within the past12months. What is the probability that 75%or more of the women in the sample have been on a diet? Follow the four-step process.

Short Answer

Expert verified

The probability that 75%or more of the women in the sample have been on a dietP(p^鈮�75%)=0.0375.

Step by step solution

01

Given Information

Given

p=70%=0.70

p^=75%=0.75

n=267

02

Explanation

The mean of the sampling distribution of p^is equal to the population proportion p:

渭p^=p=0.70

The standard deviation of the sampling distribution of p^is:

蟽p^=p(1-p)n=0.70(1-0.70)267鈮�0.0280449

The z-score is the value decreased by the mean, divided by the standard deviation:

z=x-渭蟽=0.75-0.700.0280449鈮�1.78

Determine the corresponding probability using table A:

P(p^鈮�75%)=P(z>1.78)=P(Z<-1.78)=0.0375

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Most popular questions from this chapter

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