A population has a mean of 125 and a standard deviation of 16. A sample of 64 observations will be taken. The probability that the sample mean will be between 122.4 and 126.1 is
A) 0.1821.
B) 0.0919.
C) 0.6120.
D) 0.3880.

Question

Quizplus · Accepted Answer

The standard error of the mean (SE) is calculated using the formula, SE = σ/√n, where σ is the population standard deviation and n is the sample size.

SE = 16/√64 = 2

Now, we need to standardize the sample mean using the formula, z = (x̄ - μ)/SE, where x̄ is the sample mean, μ is the population mean, and SE is the standard error of the mean.

z1 = (122.4 - 125)/2 = -0.8
z2 = (126.1 - 125)/2 = 0.55

Using the standard normal distribution table, the probability of z being between -0.8 and 0.55 is 0.6120.

Therefore, the answer is C.

A Population Has a Mean of 125 and a Standard