Question

6. The number of sick days taken by teachers in a certain school district has mean 8 and standard deviation 3. A school within the district has 25 teachers. Assuming independence, how many sick days should the school’s superintendent budget if the superintendent wants the probability of exceeding the budgeted days to be 10%

Answer 1

Probability of exceeding the budget = 10% = 0.10

µ = 8, σ=3, n=25

Therefore, P(x>8) = 0.1

z = (x-µ)/σ/n^0.5

Using standard normal tables, probability is 0.1 when z = 0.35

so, z =0.35

z = (x-µ)/σ/n^0.5 = 0.35

((x-8)/3)/25^0.5 = 0.35

(x-8)/3 = 0.35*5

(x-8)/3 = 1.75

x-8 = 1.75*3 = 5.25

x = 5.25+8 = 13.25

Sick days the school’s superintendent should budget if the superintendent wants the probability of exceeding the budgeted days to be 10% = 13.25