(FULL QUESTION BELOW) What is the probability that the mean height for the sample is greater than 65 ​inches? Assume sigma=2.81.

Question

The mean height of women in a country​ (ages 20-29) is 64.3 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 ​inches? Assume sigma=2.81.

​(Round to four decimal places as​ needed.)

Answer 1

The test statistic is (65-64.3)/(2.81)=0.2491. This corresponds to 0.5984, implying 59.84% of the heights are less than 65 inches, so 1-0.5984=0.4016 or 40.2% heights are greater than 65 inches.