Question

The salaries of the employees of a corporation are normally distributed with a mean of $26,000 and a standard deviation of $6,000. For each part, show the formula (=NORMDIST(…)) , a graph, and an explanation.

a. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation?

b. The bottom 10% of employees would pay NO income tax at all. The next 10% after this group pay only 5% of their income in taxes. Determine the cutoff point for each tax bracket:

The cutoff point (level of income $) for employees who pay no tax at all

Min

Max

The cutoff point(level of income $) for the group that pay only 5%

Min

Max

Answer 1

ANSWER:

a)

Probability that an employee will have salary of at least $35,600 P(x > 35600) = 1 - P(X<35600) =1-NORM.DIST(35600, 26000, 6000, TRUE) gives PIX > 35600) = 0.0548. 5.48% of employees have salary at least $35,600. There are 68 employees who have incomes of at least $35,600. 68/0.0548 - 1241 So, 1241 individuals are employed in the corporation.

b)

Let c be the bottom 10% of employees would pay NO income tax at all and d be the ext 10% after this group pay only 5% of their income in taxes 10% 10% C d Area below c is 10% so =NORM.INV(0.1, 26000, 6000) which gives 18310.6906 and area below d is 10% + 10% = 20%, so =NORM.INVIO.2, 26000, 6000) which gives 20950.2726 Hence, The cutoff point (level of income $) for employees who pay no tax at all Min- $0.00 Max- $18310.69 (bottom 10% mean 0 to c) The cutoff point (level of income $) for the group that pay only 5% Min-$18310.69 Max- $20950.27 (next 10% means c to d)

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