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Question
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn less than $40,000?
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Solution
Let x denotes the annual salaries of employees in a large company
Mean µ = 50,000 and S.D σ = 20,000
P(people earn less than $40,000) = P(X < 40,000)
When x = 40,000
z = `(40, 000 - 50, 000)/(20 000)`
= `(10,000)/(20,000)`
z = – 0.5
P(X < 40,000) = P(Z < – 0.5)
= P(`-oo` < z < 0) – P(– 0.5 < z < 0)
= 0.5 – P(– 0.5 < z <0)
= 0.5 – P(0 < z < 0.5) ......(Due to symmetry)
= 0.5 – 0.01915
= 0.3085
= P(X < 40,000) in percentage
= 0.3085 × 100
= 30.85
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