For a normal population with µ = 40 and σ = 10 which of the following samples is least likely to be obtained?
A)M ≤38 for a sample of n = 4
B)M ≤36 for a sample of n = 4
C)M ≤38 for a sample of n = 100
D)M ≤36 for a sample of n = 100

Question

Quizplus · Accepted Answer

As the sample size increases, the variability of the sampling distribution decreases, which means that extreme values are less likely to be obtained. Therefore, the sample with n=100 is more likely to have a mean closer to the population mean of 40. In addition, a mean of 36 is more than 2 standard deviations below the population mean, so it is a very low probability event for a normal distribution with a standard deviation of 10. Therefore, option D is the least likely sample to be obtained.

For a Normal Population with µ = 40 and σ