Answer to Question #207765 in Statistics and Probability for Mary

Question

II – PROBLEM SOLVING:(week 7)

1. The average public high school has 468

students with a standard deviation of 

87.

a) If a public school is selected, what 

is the probability that the number of 

students enrolled is greater than 

400?

b) 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

1. $\mu=468,\sigma=87$

(a) $P(X>400)=P(Z>\dfrac{400-468}{87})=P(z>-0.7816)=0.782$

(b)n=30,

$P(445<X<485)=P(\dfrac{445-468}{\frac{87}{\sqrt{38}}}<Z<\dfrac{485-468}{\frac{87}{\sqrt{38}}})\\[9pt]=P(-1.608<Z<1.188)=0.828$