A researcher selects a sample of 625 participants from a population with a mean of 120 and a standard deviation of 25.The probability of selecting a sample mean that is larger than 125 is close to zero.

Question

Quizplus · Accepted Answer

The probability of selecting a sample mean larger than 125 can be calculated by using the z-score formula, where z = (x̄ - μ) / (σ / sqrt(n)). Plugging in the given values, we get z = (125 - 120) / (25 / sqrt(625)) = 5 / 5 = 1. Since we are looking for the probability of selecting a sample mean larger than 125, we are interested in the area to the right of 125 on the normal distribution curve. Using a standard normal distribution table or calculator, we find that the probability of getting a z-score of 1 or larger is only 0.1587. Therefore, the statement is false as the probability is not close to zero.

A Researcher Selects a Sample of 625 Participants from a Population