In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a

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 54.3 inches, and standard deviation of 2.4 inches.

A) What is the probability that a randomly chosen child has a height of less than 55.7 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 49 inches?

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

Answer 1

Hi Erika,

X = heights of ten year old children in the United States of Heightlandia.

X is approximately normal with µ=54.3, σ=2.4

a. P(X<55.7) = P(Z<((55.7-54.3)/2.4) = P(Z<0.5833) = 0.720

Using TI84

Using the standard normal

normalcdf(-1000, 0.5833, 0, 1) = 0.720

or

using a normal with µ=54.3, σ=2.4

normalcdf(-1000, 55.7, 54.3, 2.4) = 0.720

b. P(X>49) = P(Z>((49-54.3)/2.4)) = P(Z>-2.208) = 0.986

Using the standard normal

normalcdf(-2.208, 1000, 0, 1) = 0.986

or

using a normal with µ=54.3, σ=2.4

normalcdf(49, 1000, 54.3, 2.4) = 0.986

Let me know if you have any questions

Dian