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If the weekly wages of 5000 workers in a factory follows normal distribution with mean and SD as Rs. 700 and Rs. 50 respectively, what is the expected number of workers with wages between Rs. 660 and Rs. 720?
  • a)
    2,050
  • b)
    2,200
  • c)
    2,218
  • d)
    2,300
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the weekly wages of 5000 workers in a factory follows normal distri...
Given data:
- Mean (μ) = Rs. 700
- Standard deviation (σ) = Rs. 50
- Number of workers (n) = 5000

We need to find the expected number of workers with wages between Rs. 660 and Rs. 720.

Approach:
We know that the weekly wages of workers follow a normal distribution. We can use the standard normal distribution to find the probability of workers having wages between Rs. 660 and Rs. 720. Then, we can use this probability to find the expected number of workers.

Let X be the random variable denoting the weekly wages of a worker. Then, X follows a normal distribution with mean (μ) and standard deviation (σ). We can standardize X to get a standard normal variable Z as follows:

Z = (X - μ) / σ

Now, we need to find the probability of workers having wages between Rs. 660 and Rs. 720. Let Z1 and Z2 be the standardized values corresponding to Rs. 660 and Rs. 720, respectively. Then,

Z1 = (660 - 700) / 50 = -0.8
Z2 = (720 - 700) / 50 = 0.4

Using a standard normal table or calculator, we can find the probabilities as follows:

P(-0.8 < z="" />< 0.4)="P(Z" />< 0.4)="" -="" p(z="" />< -0.8)="0.6554" -="" 0.2119="" />

This means that the probability of a worker having wages between Rs. 660 and Rs. 720 is 0.4435.

To find the expected number of workers with such wages, we can multiply this probability by the total number of workers. Therefore,

Expected number of workers = Probability * Number of workers
= 0.4435 * 5000
= 2,218 (approximately)

Therefore, the expected number of workers with wages between Rs. 660 and Rs. 720 is 2,218. The correct answer is option (c).
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If the weekly wages of 5000 workers in a factory follows normal distribution with mean and SD as Rs. 700 and Rs. 50 respectively, what is the expected number of workers with wages between Rs. 660 and Rs. 720?a)2,050b)2,200c)2,218d)2,300Correct answer is option 'C'. Can you explain this answer?
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If the weekly wages of 5000 workers in a factory follows normal distribution with mean and SD as Rs. 700 and Rs. 50 respectively, what is the expected number of workers with wages between Rs. 660 and Rs. 720?a)2,050b)2,200c)2,218d)2,300Correct answer is option 'C'. Can you explain this answer? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If the weekly wages of 5000 workers in a factory follows normal distribution with mean and SD as Rs. 700 and Rs. 50 respectively, what is the expected number of workers with wages between Rs. 660 and Rs. 720?a)2,050b)2,200c)2,218d)2,300Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the weekly wages of 5000 workers in a factory follows normal distribution with mean and SD as Rs. 700 and Rs. 50 respectively, what is the expected number of workers with wages between Rs. 660 and Rs. 720?a)2,050b)2,200c)2,218d)2,300Correct answer is option 'C'. Can you explain this answer?.
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