A random sample of size 100 is drawn from a population with a standard deviation of 10.If only 5% of the time a sample mean greater than 20 is obtained, the mean of the population is closest to ______
A)18.35
B)16.25
C)17.2
D)20
E)19

Question

Quizplus · Accepted Answer

The sample mean follows a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size. Given that 5% of the time the sample mean is greater than 20, we can use the z-score for 5% in the upper tail (z = 1.645) to find the population mean. Solving the equation 20 = μ + 1.645*(10/√100) gives μ ≈ 18.35.

A Random Sample of Size 100 Is Drawn from a Population