(solution) Suppose that a random variable x has normal distribution with

(solution) Suppose that a random variable x has normal distribution with

Suppose that a random variable x has normal distribution with mean=80 and standard deviation=18. Calculate the following probabilities for the sample mean if the sample size is 36.

(a) P(x<82)

(b) P(81<x<84)

Ans :?¿
Let X i , ( 1? i ? 36 ) be the iid has normal distribution withmean ?=80?¿
Standard Deviation ?=18
36 ? Xi ´
Let us define X= i=1
36 Now use Centrallimit theorem
´
X??
N…