(a) Probability that the sample mean is Greater than 64 is 0.2033 .
Step-by-step explanation:
We are given that a normal population has a mean of 62 and a standard deviation of 12 and we select a random sample of 25.
Let X bar = sample mean
The z score probability distribution for sample mean is ;
Z = ~ N(0,1)
where, = population mean = 62
= population standard deviation = 12
n = random sample = 25
So, probability that the sample mean is Greater than 64 = P(X bar > 64)
P(X bar > 64) = P( <
) = P(Z > 0.83) = 1 - P(Z <= 0.83)
= 1 - 0.79673 = 0.2033 .