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Tamil Nadu Board of Secondary EducationHSC Commerce Class 12

If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches , how many students have height less than or equal to 64 inches

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Question

If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height less than or equal to 64 inches

Sum
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Solution

Let x denote the height of a student N = 500; m = 68.0 inches and σ = 3.0 inches the standard normal variate

z = `(x - mu)/sigma = (x - 68)/3`

P(Less than or equal to 64 inches)

P(X ≤ 64)

When x = 64

z = `(64 - 68)/3 = (-4)/3 = - 1.33`

P(X ≤ 64) = P(Z ≤ – 1.33)

P(Z ≥ – 1.33)

= 0.5 – 0.4082

= 0.0918

∴ Number of heights who ate less than or equal to 64 inches

= 0.0918 × 500

= 45.9

= 46  .......(approximately)

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Chapter 7: Probability Distributions - Exercise 7.3 [Page 168]

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Samacheer Kalvi Business Mathematics and Statistics [English] Class 12 TN Board
Chapter 7 Probability Distributions
Exercise 7.3 | Q 8. (b) | Page 168

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