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 between 395.5 and 404.5 is _______.
A) 0.9756
B) 0.0244
C) 0.0278
D) 0.9722
E) 1.0000

Question

Quizplus · Accepted Answer

The probability of drawing a sample with a mean between 395.5 and 404.5 is 0.9756. This is because the mean of the sample will be normally distributed with a mean of 400 and a standard deviation of 24/sqrt(144) = 6. So, the z-score for a mean of 395.5 is (395.5 - 400) / 6 = -0.75, and the z-score for a mean of 404.5 is (404.5 - 400) / 6 = 0.75. The probability of drawing a sample with a mean between these two z-scores is 0.9756.

Suppose a Population Has a Mean of 400 and a Standard