A population of scores is normally distributed with a μ = 95 and a σ_M = 5. The probability that a randomly drawn sample of n = 12 will have a mean of 88 or above is _________. A) .0808 B) .9192 C) .7190 D) .2810

Question

Quizplus · Accepted Answer

We need to find the probability of obtaining a sample mean of 88 or above which can be calculated using the z-score formula for sample means:

z = (M - μ) / (σ / sqrt(n))

where M is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values, we get:

z = (88 - 95) / (5 / sqrt(12))
z = -2.19

Using a standard normal distribution table, we can find the probability of a z-score less than -2.19 which is the same as the probability of a z-score greater than 2.19 (since the normal distribution is symmetrical). This probability is approximately 0.014.

Therefore, the probability of obtaining a sample mean of 88 or above is 1 - 0.014 = 0.986 or 98.6%.

The closest answer choice is B, which is 0.9192.

A Population of Scores Is Normally Distributed with a μ