Question 1159021: 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.
Answer by ikleyn(53996)   (Show Source):
You can put this solution on YOUR website! .
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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You may calculate the standard z-score
z =  = 0.8929 (rounded with 4 decimals)
and then find the area under the standard normal curve on the left of this z-score using the normal table.
Since you are looking for the probability to be on the right of the score $48000,
do not forget to take the COMPLEMENT to the value from the table.
Alternatively, you may use the standard function normaldist in your TI-84 calculator
min-score, score mean SD <<<---=== formatting pattern
p = 1 - normalcdf( 0, 48000, 41750, 7000).
You will get the value p = 0.186.
Even faster/easier alternative is to use an online free of charge calculator at website
https://onlinestatbook.com/2/calculators/normal_dist.html/
It gives the same value of probability p = 0.186.
In addition, this calculator provides you the plot, so you can see the area visually.
In this sense, this online calculator is the best teacher for such kind of problems.
ANSWER. The desired "proportion" (or the probability) is 0.186.
Solved.
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