According to a recent survey, the salaries of assistant professors have a mean of $41,750 and a standard deviation of $7000. assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn more than $48,000. round your answer to at least four decimal places.

Question

Uriah Herrera

Mathematics

28 December, 01:53

According to a recent survey, the salaries of assistant professors have a mean of $41,750 and a standard deviation of $7000. assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn more than $48,000. round your answer to at least four decimal places.

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Cameron Robinson · Answer 1

To get the proportion of professors who earn more than $ 48,000 we proceed as follows;

z = (x-mean) / s. d

x=48000

mean=41,750

s. d=7000

thus;

z = (48000-41750) / 7000

=0.8929

the probability associated with z-score is:

P (48000) = 0.8133

thus the probabilty of those who are earning more than $48,000 will be:

1-0.8133

=0.1867