A population of unknown shape has a mean of 75. You select a sample of 40. The standard deviation of the sample is 5. Compute the probability the sample mean is:
a. Less than 74.
b. Between 74 and 76.
c. Between 76 and 77.
d. Greater than 77.
Assuming that Central Limit Theorem holds,and use the z distribution tables for calculations:
For this problem the STD of the sample mean is 5/sqrt(40) = 0.7906 .
So we have a normal distributed ramdom variable X with mean Mu = 75
and standard deviation StD = 0.7906
-Compute the probability the sample ...
This solution explains how the central limit theorem is used to estimate the mean of a sample based on information about the population.