Question

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 57 inches, and standard deviation of 7.4 inches.

What is the probability that the height of a randomly chosen child is between 65 and 72.6 inches? ___________

(Round your answer to 4 decimal places.)

Answer 1

Here, μ = 57, σ = 7.4, x1 = 65 and x2 = 72.6. We need to compute P(65<= X <= 72.6). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (65 - 57)/7.4 = 1.08
z2 = (72.6 - 57)/7.4 = 2.11

Therefore, we get
P(65 <= X <= 72.6) = P((72.6 - 57)/7.4) <= z <= (72.6 - 57)/7.4)
= P(1.08 <= z <= 2.11) = P(z <= 2.11) - P(z <= 1.08)
= 0.9826 - 0.8599
= 0.1227