What is the probability

Question

Studies have shown that girls at age 3 have heights that are normally distributed with a mean of 37 inches and a standard deviation of 3.5 inches.

c. What is the probability that a 3-year-old girl is 46 inches tall?

Answer 1

z score = (46-37)/3.5 = 9/3.5 = 18/7 = about 2.571

use a z score calculator

Pr(<46 inches) = 99.493%

Pr(>46 inches) = 0.507%

Pr(exactly 46 inches) = exactly 0% chance

but "46 inches" probably means rounded off to nearest inch, so find the probability

Pr(45.5<x<46.5)

use a z score calculator for (46.5-37)/3.5 = 2.7142 and for (45.5-37)/3.5 = 2.4286

find the area between those 2 z values

Pr(45.5<x<46.5) = 0.4257% = less than one half of one percent chance