A sample of size 45 will be drawn from a population with mean 10 and standard deviation 5 . Find the probability that $\bar { x }$ will be greater than 11 .
A) 0.1170
B) 0.0901
C) 0.9099
D) 0.0721

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean $\bar{x}$ is normally distributed with mean 10 and standard deviation $\frac{5}{\sqrt{45}}$. To find the probability that $\bar{x} > 11$, we calculate the z-score: $z = \frac{11 - 10}{5/\sqrt{45}} \approx 1.34$. Using the standard normal distribution table, the probability of z being greater than 1.34 is approximately 0.0901.

A Sample of Size 45 Will Be Drawn from a Population