a) State three properties of a normal distribution. b) The personnel manager for
ID: 3331822 • Letter: A
Question
a) State three properties of a normal distribution.
b) The personnel manager for a large company is interested in the distribution of sick-leave hours for employees of the company. A recent study revealed the distribution to be normal, with a mean of 58 hours per year and a standard deviation of 14 hours. It is company policy that the first 40 hours of sick leave per year will be paid, with any sick-leave hours over 40 being without pay.
i. What is the probability that an employee will use between 74 and 90 hours of sick leave in a year?
ii. What proportion of employees will incur some unpaid sick leave during the year?
iii. The company is considering a change to its paid sick leave policy. How many sick-leave hours (in whole hours) should be paid by the company so that at most 10% of employees will incur some unpaid sick leave during the year.
Explanation / Answer
a.
The normal curve is symmetrical about the mean . The mean is at the middle and divides the area into halves;
The total area under the curve is equal to 1;
It is completely determined by its mean and standard deviation (or variance 2)
b. Mean = 58, Stdev = 14
i) P(74<X<90) = P(74-58/14<Z< 90-58/14)=.9888-.9568 = 0.0321
ii)P(X>40) = P(Z> 40-58/ 14) = P(Z> -18/14) =. 9007 or 90.97%
iii) P(X<=c) = .10, Z = -1.28, So, X = -1.28*14+58 = 40.08 or 40
These many sick-leave hours (in whole hours) should be paid by the company so that at most 10% of employees will incur some unpaid sick leave during the year.
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