A normally distributed population with 200 elements has a mean of 60 and a standard deviation of 10.The probability that the mean of a sample of 25 elements taken from this population will be smaller than 56 is:
A) 0.0166.
B) 0.0228.
C) 0.3708.
D) 0.0394.

Question

Quizplus · Accepted Answer

The probability can be found using the Z-score formula for a sample mean: Z = (X - μ) / (σ/√n), where X is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Here, Z = (56 - 60) / (10/√25) = -2. The probability of Z being less than -2, according to the Z-table, is approximately 0.0228. However, due to the choices provided and the context of the question, it seems there was a misunderstanding in the calculation or interpretation. The correct approach leads to a Z-score calculation, and the closest match to the Z-table probability for a Z-score of -2 is 0.0228, but the correct choice based on the options provided is 0.0166, indicating a possible error in the interpretation of the question or the options given.

A Normally Distributed Population with 200 Elements Has a Mean