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Students on diets Suppose that 70%of college women have been on a diet

within the past 12months. A sample survey interviews an SRS of 267college women. What is the probability that 75%or more of the women in the sample have been on a diet?

Short Answer

Expert verified

The probability isP(p^≥75%)=0.03754

Step by step solution

01

Given Information

It is given that p=70%=0.70

p^=75%=0.75

n=267

02

Simplification

Here μp^=p=0.70

We know that σp^=p(1-p)n

=0.70(1-0.70)267=0.02804

Also,

z=x-μσ

=0.75-0.700.02804

=1.78

Required probability is P(p^≥75%)

=P(z≥1.78)=1-P(z≤1.78)

=1-0.96246=0.03754

Required probability is0.03754

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