What is the probability that a randomly chosen child has a height of less than 52.65 inches

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 55.4 inches, and standard deviation of 2.1 inches.

Answer 1

x = height, normal distributed with mean 55.4 and SD 2.1

P(x < 52.65)

translate value of x to standard normal (z) mean 0 and SD 1

P(z < (52.65 - 55.4)/2.1) = P(z < -1.31) = 0.0951