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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 more than $75,000
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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
Standard normal variate z = `(x - mu)/sigma`
P(people earn more than$75,000) = P(X > 70000)
When x = 75,000
z = `(75,000 - 50, 000)/(20,000)`
= `25000/20000`
= `5/4`
z = 1.25
P(X > 75,000) = P(X > 1.25)
= P(0 < z < `oo`) – P(0 < z < 1.25)
= 0.5 – 0.3944
= 0.1056
P(x > 750,000) in percent
= 01056 × 100
= 10.56
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