SOLUTION: Given a normal distribution with μ = 100 and σ = 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

Question 1165890: Given a normal distribution with μ = 100 and σ = 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?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
z=(x bar-mu)/sigma/sqrt(n)
<95 is (95-100)/10/5, and that is -5/2 or -2.5. Probability is 0.0062
between 95 and 97.5 is between z=-2.5 and -1.5, since the SEM is 2. That probability is 0.0606.
above 102.2 is z>2.2/2 or 1.1. Probability is 0.1357
the 35th percentile is at z=-0.39
so 65% of the area is above that
-0.39=(x-100)/2
-0.78=x-100
x=99.22
so 65% chance the sample mean is above 99.2 (rounded)

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