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 54.9 inches, and standard deviation of 4 inches.

A) What is the probability that a randomly chosen child has a height of less than 56.6 inches?


B) What is the probability that a randomly chosen child has a height of more than 51.1 inches?

Answer 1

Let X : height of 10 year old children is approximately normal with mean = 54.9 and standard deviation = 4 inches

A) P( X < 56.6) = P[ ( X - )/ < ( 56.6 - 54.9)/4]

P( X < 56.6) = P( Z < 0.43)

Using Z table

P( X < 56.6) = 0.6664

B) P( X > 51.1) = P[ ( X - )/ > (51.1 - 54.9)/4]

P( X > 51.1) = P( Z > -0.95)

P( X > 51.1) = 0.8289