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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 greater than 72 inches
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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(Greater than 72 inches)
P = P(X > 72)
When x = 72
z = `(72 - 68)/3 = 4/3` = 1.33
P(x > 72) = P(z > 1.33)
= 0.5 – 0.4082
= 0.0918
Number of students whose height are greater than 72 inches
= 0.0918 × 500
= 45.9
= 46 ......(approximately)
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