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Chapter 7: Q. 40 (page 441)

Harley-Davidson motorcycles make up 14%of all the motorcycles registered in the United States. You plan to interview an SRS of500 motorcycle owners. How likely is your sample to contain 20% or more who own Harleys? Follow the four-step process.

Short Answer

Expert verified

P(p^≥20%)=0.0001

Step by step solution

01

Given Information

Given

p=14%=0.14

p^=20%=0.20

n=500

02

Explanation

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

μp^=p=0.14

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

localid="1650090879636" σp^=p(1-p)n=0.14(1-0.14)500≈0.0155177

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

localid="1650090933246" z=x-μσ=0.20-0.140.0155177≈3.87

Determine the corresponding probability using table A:

localid="1650090960373" P(p^≥20%)=P(z>3.87)=P(Z<-3.87)=0.0001

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