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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

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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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?

Sum
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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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Chapter 7: Probability Distributions - Miscellaneous problems [Page 172]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 7 Probability Distributions
Miscellaneous problems | Q 7. (a) | Page 172

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