The probability of having six leave time for next month falling between 50 and 80 hours is 0.152
Standard deviation, σ = 20 hours
Mean, μ = 100 hours
The probability that sick leave time for next month will be between 50 and 80 hours can be expressed thus :
Recall :
Zscore = (x - μ) / σ
P(50 ≤ X ≤ 80) = P(Z < (80 - 100)/20)) - P(Z < (50 - 100)/20))
P(50 ≤ X ≤ 80) = P(Z < - 1) - P(Z < - 2.5)
Using the normal distribution table :
P(Z < - 1) = 0.15866
P(Z < - 2.5) = 0.0062097
Hence,
P(-1 ≤ Z ≤ - 2.5) = P(Z < - 1) - P(Z < - 2.5) = 0.15866 - 0.0062097 = 0.1524
Therefore, the probability of having sick leave time between 50 and 80 hours next month is 0.152
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