Question

5.4.15 Question Help 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 n = 68, find the probability of a sample mean being less than 22.1 if u = 22 and o=1.31. Click the icon to view page 1 of the standard normal table. Click the icon to view page 2 of the standard normal table. For a sample of n = 68, the probability of a sample mean being less than 22.1 if p = 22 and a = 1.31 is .. (Round to four decimal places as needed.)

Answer 1

solution:

the given information as follows:

mean = $\mu$ = 22

SD = $\sigma$ = 1.31

sample size = n = 68

we have to find the probability that sample mean is less than 22.1 = $P(\bar X < 22.1)$

so corresponding z score as follows:

$z = \frac{\bar X-\mu}{\sigma/\sqrt{n}}=\frac{22.1-22}{1.31/\sqrt{68}}=0.63$

$P(\bar X < 22.1)$ = value of z to the left of 0.63 from the standard normal table = 0.7357

so, probability that sample mean is less than 22.1 = 0.7357

0.7357 22 22.1