3. The weekly wages of 1000 workmen are normally distributed around a mean of Rs.70 with a S.D. of Rs.5. Estimate the number of workers , whose weekly wages will be between Rs.69 and Rs.72.
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Answer: 235
Step-by-step explanation:
Given data:
N = 1000
Mean wage, µ = Rs. 70
The standard deviation of wages, σ = Rs. 5
To find: no. of workers whose weekly wages will be between Rs. 69 & Rs. 72
Solution:
Here, X1 = Rs. 69 and X2 = Rs. 72
Z1 = (X1 - µ)/σ = (69 – 70) / 5 = -1/5 = -0.2
Z2 = (X2 - µ)/σ = (72 - 70)/5 = 2/5 = 0.4
Now,
Probability of a person having wages between Rs. 69 to Rs. 72 is,
= P(Z1 <= Z <= Z2)
= P(-0.2 <= Z <= 0.4)
= P(-0.2 <= Z <= 0) + P(0<= Z <= 0.4)
= P(0<= Z <= 0.2) + P(0<= Z <= 0.4)
= ZTable (0.2) + ZTable (0.4)
= 0.0793 + 0.1554
= 0.2347
∴ Number of persons with wages between Rs 69 and Rs 72 is,
= N * Probability
= 1000 * 0.2347
= 234.7
≈ 235
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