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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 between 65 and 71 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(Between 65 and 71 inches)
P(65 ≤ x ≤ 71)
When x = 65
z = `(65 - 68)/3 = (-3)/3 = - 1`
When x = 71
z = `(71 - 68)/3 = 3/3` = 1
P(65 ≤ x ≤ 71) = P(– 1 < z < 1)
= P(– 1 < z < 0) + P(0 < z < 1)
= P(0 < z < 1) + P(0 < z < 1)
= 2 × [P(0 < z < 1)]
= 2 × 0.3413
= 0.6826
∴ Number of students whose height between 65 and 7 inches
= 0.6826 × 500
= 341.3
= 342 .......(approximately)
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