A random sample of n = 4 scores is obtained from a normal population with µ = 30 and σ = 8.What is the probability that the sample mean will be smaller than M = 22?
A)0.00003
B)0.0228
C)0.1587
D)0.3085

Question

Quizplus · Accepted Answer

The probability that the sample mean will be smaller than M = 22 can be found using the z-score formula for a sample mean: $z = \frac{M - \mu}{\sigma/\sqrt{n}}$, where M is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{22 - 30}{8/\sqrt{4}} = \frac{-8}{4} = -2$. Looking up a z-score of -2 in the standard normal distribution table gives a probability of approximately 0.0228.

A Random Sample of N = 4 Scores Is Obtained