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The salary of workers of a factory is known to follow normal distribution with an average salary of 10,000 and standard deviation of salary as 2,000. If 50 workers receive salary more than 14,000, then the total no. of workers in the factory is (a) 2,193 (b) 2,000 (c) 2,200 (d) 2,500?
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The salary of workers of a factory is known to follow normal distribut...
Solution:

Given, the average salary of workers of a factory is 10,000 and standard deviation as 2,000.

Let X be the salary of workers in the factory.

Hence, X ~ N(10,000, 2,000^2)

To find the total number of workers in the factory, we need to find the total number of workers who receive salary less than or equal to 14,000.

Let Z be the standard normal variable, then

Z = (X - 10,000)/2,000

P(X > 14,000) = P(Z > (14,000 - 10,000)/2,000)

= P(Z > 2)

= 0.0228 (using standard normal distribution table)

Therefore, the probability that a worker receives salary more than 14,000 is 0.0228.

Let N be the total number of workers in the factory.

Then, the number of workers who receive salary more than 14,000 is N x 0.0228.

Given that 50 workers receive salary more than 14,000.

Therefore, N x 0.0228 = 50

N = 50/0.0228

N = 2,192.98

Hence, the total number of workers in the factory is approximately 2,193.

Therefore, the correct option is (a) 2,193.
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The salary of workers of a factory is known to follow normal distribution with an average salary of 10,000 and standard deviation of salary as 2,000. If 50 workers receive salary more than 14,000, then the total no. of workers in the factory is (a) 2,193 (b) 2,000 (c) 2,200 (d) 2,500?
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The salary of workers of a factory is known to follow normal distribution with an average salary of 10,000 and standard deviation of salary as 2,000. If 50 workers receive salary more than 14,000, then the total no. of workers in the factory is (a) 2,193 (b) 2,000 (c) 2,200 (d) 2,500? for Commerce 2024 is part of Commerce preparation. The Question and answers have been prepared according to the Commerce exam syllabus. Information about The salary of workers of a factory is known to follow normal distribution with an average salary of 10,000 and standard deviation of salary as 2,000. If 50 workers receive salary more than 14,000, then the total no. of workers in the factory is (a) 2,193 (b) 2,000 (c) 2,200 (d) 2,500? covers all topics & solutions for Commerce 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The salary of workers of a factory is known to follow normal distribution with an average salary of 10,000 and standard deviation of salary as 2,000. If 50 workers receive salary more than 14,000, then the total no. of workers in the factory is (a) 2,193 (b) 2,000 (c) 2,200 (d) 2,500?.
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