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

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distributed with a mean of 54.8 inches, and standard deviation of
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inches?

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