Question

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.

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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