The salaries of the employees of a corporation are normally distributed with a m

Question

The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation? A) 4,000 B) 2,500 C) 2,000 D) 4,100 The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation? A) 4,000 B) 2,500 C) 2,000 D) 4,100

Explanation / Answer

AS GIVEN THE DISTRIBUTION IS NORMALLY DISTRIBUTED

WITH MEAN = 25000

STANDARD DEVIATION =5000

IT IS GIVEN THAT TOTAL NUMBER OF PEOPLE HAVE CERTAIN AMOUNT OF MONEY

NOW TO BE FOUND THE TOTAL WRKFORCE

P(X>= 35600) = Z = (35600 - 25000)/5000 = 2.12

THEREFORE

P(Z>35600) = P(Z>2.12) = TOTAL AREA - AREA OF Z>2.12

THEREFORE 1 - 0.9830 = 0.017

THEREFORE 1.17% PEOPLE HAVE SALARY OF 35600

AS GIVEN 1.17% = 68

THEREFORE TOTAL WORKFORCE = 68/0.017

= 4000

OPTION A IS CORRECT.

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