# Normal Distribution and Probabilities

Given a normal distribution with a mean of 100 and a standard deviation of 10, if you select a sample of n = 25, what is the probability that the sample mean is a. less than 95? b. between 95 and 97.5? c. above ?102.2? d. There is a 65% chance that the sample mean is above what value?

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#### Solution Preview

a. z=(95-100)/(10/sqrt(25))=-2.5

P(z<-2.5)=0.0062

b. ...

#### Solution Summary

The expert examines normal distribution and probabilities.

$2.19