Answer to Question #207765 in Statistics and Probability for Mary

Question #207765

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?



1
Expert's answer
2021-06-21T10:47:55-0400
  1. μ=468,σ=87\mu=468,\sigma=87


(a) P(X>400)=P(Z>40046887)=P(z>0.7816)=0.782P(X>400)=P(Z>\dfrac{400-468}{87})=P(z>-0.7816)=0.782


(b)n=30,


P(445<X<485)=P(4454688738<Z<4854688738)=P(1.608<Z<1.188)=0.828P(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


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