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 n=70, find the probability of a sample mean being greater than 211 if p = 210 and 6 = 3.5. For a sample of n=70, the probability of a sample mean being greater than 211 if = 210 and a 3.5 is (Round to four decimal places as needed.) Would the given sample mean be considered unusual? The sample mean be considered unusual because it within the range of a usual event, namely within mean of the sample means. of the

Answer 1

$\mu$ = 210

$\sigma$ = 3.5

n = 70

SE = $\sigma$ /$\sqrt{n}$

= 3.5/

V70

= 0.4183

To find P($\tilde{x}$ > 211):

Z = (211 - 210)/0.4183

= 2.3905

By Technology, Cumulative Area Under Standard Normal Curve = 0.9916

So,

P($\tilde{x}$ > 211): = 1 - 0.9916 = 0.0084 = 0.84% < 5%

For a sample of n = 70, the probability of a sample mean being greater than 211 if $\mu$ = 210 and $\sigma$ = 3.5 is 0.0084.

The sample mean would be considered unusual because it is not within the range of a usual event,namely within two standard deviation of the mea of the sample means.