DESCRIPTIVE STATISTICS

Question

n the country of the United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.1 inches, and a standard deviation of 3.5 inches.

A) What is the probability that a randomly chosen child has a height of less than 46.65 inches?

Answer= (Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 51 inches?

Answer= (Round your answer to 3 decimal places.)

Answer 1

On this type of question you want to first use the formula

z = (x – mean) / (standard deviation) in order to convert the given values over into a Z score. then once you have done that you can use technology like a calculator or Microsoft Excel to convert the value over into a probability

From the values in the question we get

z = (46.65 – 55.1)/3.5 = -2.4

z = (51 – 55.1)/3.5 = -1.17

for the Z values

using technology to convert that over then I get 0.008 for P(Z < -2.4) and then 0.879 for P(Z > -1.17)