Question

PLEASE ANSWER ALL PARTS AND SHOW ALL WORK

Unless otherwise specified, please use alpha = 0.05.

According to the 2012–2013 annual report of the American Psychological Association’s survey of faculty salaries in graduate departments of psychology, the average salary for a new (less than 3 years) professor was $92,000, with a standard deviation of $32,845. Assuming that these data are normally distributed:

- What was the salary for a new full professor in the 76th percentile?

- What percentage of new professors earn less than $50,000?

Answer 1

Solution:

Given that,

mean = = 92000

standard deviation = = 32845

Using standard normal table,

A ) P(Z < z) = 76%

P(Z < z) = 0.76

P(Z < 0.7063) = 0.76

z = 0.7063

Using z-score formula,

= z * +

= 0.7063 * 32845 + 92000

= 115198.4235

The 76t^h percentile = 115198 .42

B ) p ( x < 50000 )

= p ( x -  / ) < ( 50000 - 92000 / 32845)

= p ( z < - 87000 / 32845 )

= p ( z < - 2.65 )

Using z table

= 0.0040

Probability = 0.0040 = 0.40%