Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population,the probability of drawing a sample with a mean of more than 404.5 is _______.
A) 0.0139
B) 0.4861
C) 0.4878
D) 0.0122
E) 0.5000

Question

Quizplus · Accepted Answer

The standard error of the mean (SEM) is calculated as the population standard deviation divided by the square root of the sample size: SEM = 24 / √144 = 2. The z-score for a sample mean of 404.5 is (404.5 - 400) / 2 = 2.25. Using the standard normal distribution table, the probability of a z-score greater than 2.25 is approximately 0.0122.

Suppose a Population Has a Mean of 400 and a Standard