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Chapter 8: Q.55 (page 518)

The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI M in this population to within ±1vwith 99% confidence? Show your work.

Short Answer

Expert verified

sample sizen=373

Step by step solution

01

Given information 

Given in the question that, The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5.

02

Explanation

Given,

E=1

σ=7.5

sample size

For confidence level 1-α=0.99, determine zα/2=z0.005using table A (look up 0.005in the table, the z-score is then the found z-score with opposite sign):

zα/2=2.575

localid="1650094028575" n=zα/2σE2=2.575×7.512≈373

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