Question

suppose that heights of a 10 year old boys and girls closely follow a normal distribution with mean 51 inches and standard deviation 2 inches

a. what percentage of 10 year olds are shorter than 50 inches?
b. What percentage of 10 year olds fall between 48 and 54 inches?

Answer 1

normal distribution with mean 51 inches andstandard deviation 2 inches:
f (x, mean, sigma)
where:
mean - 51 inches,
sigma - standard deviation - 2 inches
a)
percentage of 10 year olds is shorter than 50 inches:
x<50 => x (-Infinity, 50)
Therefore:
Integrate [ f(x, mean, sigma), {x, -Infinity, 50}] = 0.308538= 31%
b)
percentage of 10 year olds falls between 48 and 54inches:
48<x<54 => x (48, 54)
Therefore:
Integrate [ f(x, mean, sigma), {x, 48, 54}] = 0.866386 = 87%