Question

the population mean and standard deviation are given below. find the indicated probability and determine whether the given sample mean would be considered unusual.
for a sample of n = 40, find the probability of a sample mean being less than 12,750 or greater than 12,753 when μ = 12,750 and σ = 1.4.
for the given sample, the probability of a sample mean being less than 12,750 or greater than 12,753 is 0.5000 (round to four decimal places as needed.)
would the given sample mean be considered unusual?
a. the sample mean would not be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.
b. the sample mean would not be considered unusual because there is a probability less than 0.05 of the sample mean being within this range.
c. the sample mean would be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.
d. the sample mean would be considered unusual because there is a probability less than 0.05 of the sample mean being within this range.

Explanation:

Step1: Recall the rule for unusual events

In statistics, an event with a probability less than 0.05 is considered unusual. The probability of the sample - mean being less than 12750 or greater than 12753 is 0.5000.

Step2: Determine if the event is unusual

Since 0.5000>0.05, the sample mean is not unusual.

Answer:

A. The sample mean would not be considered unusual because there is a probability greater than 0.05 of the sample mean being within this range.