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 ______
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 the sample mean is greater than 20 only 5% of the time, we can use the z-score for 95% (1.645) to find the population mean: 20 = μ + 1.645*(10/√100), solving gives μ ≈ 18.35.

A Random Sample of Size 100 Is Drawn from a Population