13 Probability 13 Suppose that X X does only the top 12 ex

13.

Probability =

13. Suppose that X = X does only the top 12% exceed? X is greater than 170.5? Probability = B. What value of X is normally distributed with mean 115 and standard deviation 30. A. What is the probability that

Solution

(A) P(X>170.5) = P((X-mean)/s >(170.5-115)/30)

=P(Z>1.85) =0.0322 (from standard normal table)

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(B)P(X>x)=0.12

--> P(Z<(x-115)/30) =1-0.12=0.88

--> (x-115)/30 = 1.17 (from standard normal table)

So x= 115+1.17*30=150.1