Suppose that the sick leave taken by the typical worker per year has
= 10,
= 2, measured in days. A firm has n = 30 employees. Assuming independence, how many sick days should the firm budget if the financial officer wants the probability of exceeding the number of days budgeted to be less than 20%.
EXPERT ANSWER
Solution,
Given that,
mean = 
= 10
standard deviation = 
= 2
n = 30
= = 10
= / 
n = 2 / 30 = 0.37
Using standard normal table,
P(Z > z) = 20%
=1 – P(Z < z ) = 0.20
= P(Z < z ) = 1 – 0.20
= P(Z < 0.84 ) = 0.80
z = 0.84
Using z-score formula
= z * +
= 0.84 * 0.37 + 10
= 10.31 days