A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is
A)0
B).0495
C).4505
D).9505

Question

Quizplus · Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample mean, which we know to be normally distributed with mean equal to the population mean (53) and standard deviation equal to the population standard deviation divided by the square root of the sample size (21/sqrt(49) = 3).

So, we want to find the probability that a sample mean from this distribution is greater than 57.95:

z = (57.95 - 53) / 3 = 1.65

Using a standard normal distribution table or calculator, we can find that the probability of a value being greater than 1.65 is approximately 0.0495. Therefore, the answer is B.

A Population Has a Mean of 53 and a Standard