Question

Students on diets A sample survey interviews an SRS of $267$college women. Suppose (as is roughly true) that $70\%$ of college women have been on a diet within the past $12$ months. 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

The probability that $75\%$or more of the women in the sample have been on a diet is$0.0375.$

Step-by-step solution

Given Information 

Number of $SRS=267$

The proportion of women on a diet within the past $12$months $=70\%$

Explanation 

We have,

$p=70\%=0.70$

$\hat{p}=75\%=0.75$

$n=267$

$\hat{p}$ is equal to the percentage of the population $p$ in the sampling distribution: