A random sample of n = 9 scores is obtained from a normal population with µ = 40 and σ = 18.What is the probability that the sample mean will be greater than M = 43?
A)0.4325
B)0.3085
C)0.1587
D)0.0228

Question

Quizplus · Accepted Answer

The probability that the sample mean will be greater than 43 can be found using the z-score formula for a sample mean: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ 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: $z = \frac{43 - 40}{18/\sqrt{9}} = \frac{3}{6} = 0.5$. Looking up 0.5 on the standard normal distribution table or using a calculator gives a right-tail probability of approximately 0.3085.

A Random Sample of N = 9 Scores Is Obtained