Answer to Question #197717 in Statistics and Probability for Jay

Question

The average public elementary school has 468 students with a standard deviation of 87. If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is between 445 and 485?

Answer 1

$P(445<\bar X<485)=P(\frac{445-468}{\frac{87}{\sqrt{38}}}<Z<\frac{485-468}{\frac{87}{\sqrt{38}}})=$

$=P(-1.63<Z<1.20)=P(Z<1.20)-P(Z<-1.63)=$

$=P(Z<1.20)-1+P(Z<1.63)=0.8849-1+0.9484=0.8333.$