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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 53.3 inches, and standard deviation of 1 inches.

What is the probability that the height of a randomly chosen child is between 53.3 and 55.3 inches

Answer 1

use the empirical rule: 668-95-99.7 % are within 1,2 or 3 standard deviations from the mean

divide 95 by 2 to get 47.5% between 53.5 and 55.5 inches

95% is between 51.5 and 55.5. half as much is between 53.5 and 55.5

that's a very close approximation. For a closer answer use a z calculator such as Desmos.

plug in left z score of 0 and right z score of 2 and it spits out the solution along with a graph.

It also calculates the z scores for you from the mean and standard deviation.