A sample of n = 25 scores is selected from a population with μ = 70 and σ = 20.It is very unlikely that the sample mean will be smaller than 72.

Question

Quizplus · Accepted Answer

We can use the central limit theorem to determine the probability of the sample mean being smaller than 72. The formula is:

z = (x - μ) / (σ / sqrt(n))

Where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size. Plugging in the values, we get:

z = (72 - 70) / (20 / sqrt(25)) = 1

Using a standard normal table, the probability of z being less than 1 is approximately 0.32. Therefore, there is a 32% chance that the sample mean will be smaller than 72. This is not very unlikely, so the answer is false.

A Sample of N = 25 Scores Is Selected from a Population