Question

The weekly wages of 2000 workers are normally distributed. its mean and standard deviation are rs. 140 and rs. 10 respectively. Estimate the number of workers whose weekly wages will be:

I) between Rs. 120 and Rs. 130
II) more than Rs. 170
III) less than Rs. 165

Answer 1

To estimate the number of workers whose weekly wages fall within a certain range, we can use the Z-score formula. The Z-scores and probabilities for the given wage ranges are as follows: I) Between Rs. 120 and Rs. 130: Probability = 0.1587, II) More than Rs. 170: Probability = 0.0013, III) Less than Rs. 165: Probability = 0.9938.

Step-by-step explanation:

To estimate the number of workers whose weekly wages fall within a certain range, we can use the Z-score formula. The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

To estimate the number of workers whose weekly wages will be between Rs. 120 and Rs. 130, we can calculate the Z-scores for these values and use a Z-table to find the probabilities. For more than Rs. 170, we can calculate the Z-score for Rs. 170 and find the probability to the right of that Z-score. For less than Rs. 165, we can calculate the Z-score for Rs. 165 and find the probability to the left of that Z-score.

Let's calculate the Z-scores and find the probabilities:

I) Between Rs. 120 and Rs. 130:

Z-score for Rs. 120: (120 - 140) / 10 = -2

Z-score for Rs. 130: (130 - 140) / 10 = -1

Probability between Rs. 120 and Rs. 130 = P(-2 < Z < -1)

Using a Z-table, we find the probability to be approximately 0.1587.

II) More than Rs. 170:

Z-score for Rs. 170: (170 - 140) / 10 = 3

Probability more than Rs. 170 = P(Z > 3)

Using a Z-table, we find the probability to be approximately 0.0013.

III) Less than Rs. 165:

Z-score for Rs. 165: (165 - 140) / 10 = 2.5

Probability less than Rs. 165 = P(Z < 2.5)

Using a Z-table, we find the probability to be approximately 0.9938.