Answer to Question #203350 in Statistics and Probability for MACLANG, REANA LEI

Question

1.  If a random sample of 38 public elementary schools is selected , what is the probability

 That the number of students enrolled is will be more than 400 ?

Answer 1

If a random sample of n=38 public elementary schools is selected, then the average number of students enrolled would be a normally distributed random variable $Y$ with the mean $\mu=468$ and the standard deviation $\sigma/\sqrt{n}=87/\sqrt{38}.$

$$P(Y>400)=1-P(Y\leq400)$$

$$=1-P(Z\leq\dfrac{400-468}{87/\sqrt{38}})\approx1-P(Z\leq-4.818163)$$

$$\approx0.9999993$$