Question

According to a recent survey, the salaries of assistant professors have a mean of $40,756. and...

According to a recent survey, the salaries of assistant professors have a mean of $40,756. and a standard deviation of $8000. Assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn less than $42,000. Round your answer to at least four decimal places.

Math   Statistics-And-Probability   
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Answer #1

Solution:

Given, the Normal distribution with,

   = 40756

= 8000

Find P(X < 42000)

P(X< 42000) = P[(X - )/ <  (75 - )/]

= P[Z <  (42000 - 40756)/8000]

= P[Z < 0.156]

=   0.5620 ( use z table)

The proportion of assistant professors who earn less than $42,000 is   0.5620

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