Can anyone show me the details for this problem? i know the answers but i dont know how to get them.?

Question

A sample of 100 of the 2000 faculty members at Ohio State University had a mean income of $62,000 with a standard deviation of $8,000. What is your best estimate for the number of all faculty members who earn between $50,000 and $72,000? What salaries would be considered outliers?

Answer 1

find the arithmetic mean - $62,000

Data like this typically approximates normally distributed population think bell curve. About 68% of the values are within 1 standard deviation of the mean, about 95% of the values are within two standard deviations and about 99.7% lie within 3 standard deviations.

62,000

>78,000 outlier

78000 +2 SD

70000 +1 SD

62000 - mean  68% fall +/- 1 SD

54000 -1 SD

46000 -2 SD

68% are 1 SD so, 68% of 2000 employees = 1360

5% are outliers, greater than 2 SD

outlier salaries are under $46,000 and over $78,000