Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of nequals65​, find the probability of a sample mean being greater than 213 if muequals212 and sigmaequals5.8.

Answer 1

Answer: Not unusual.

Step-by-step explanation:

We know that the  z-scores lower than -1.96 or higher than 1.96 are considered as unusual.

Given : Sample size : n= 65

Sample mean = $\mu= 212$

Standard deviation : $\sigma=5.8$

Formula for z-score : $z=\dfrac{x-\mu}{\sigma}$

At x= 213

$z=\dfrac{213-212}{5.8}=0.172413793103\approx0.17$

Since , -1.96< 0.17 <1.96

It means the probability of a sample mean being greater than 213 is not unusual.