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 53.5 inches, and standard deviation of 7.3 inches.
A) What is the probability that a randomly chosen child has a height of less than 52.85 inches?
B) What is the probability that a randomly chosen child has a height of more than 46.8 inches?

Answer 1

Answer:

A) 0.46452

B) 0.82064

Step-by-step explanation:

We solve for question A and B using z score formula

z = (x - μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation.

A) What is the probability that a randomly chosen child has a height of less than 52.85 inches?

x = 52.85 inches, μ = 53.5 inches, σ = 7.3 inches

z = (x - μ)/σ

= 52.85 - 53.5 / 7.3

= -0.08904

Using the z table to find the probability of the z score above.

P(x<52.85) = 0.46452

Therefore, the probability that a randomly chosen child has a height of less than 52.85 inches is 0.46452

B) What is the probability that a randomly chosen child has a height of more than 46.8 inches?

x = 46.8 inches, μ = 53.5 inches, σ = 7.3 inches

z = (x - μ)/σ

= 46.8 - 53.5 / 7.3

= -0.91781

Using the z table to find the probability of the z score above.

P(x<46.8) = 0.17936

P(x>46.8) = 1 - P(x<46.8)

= 1 - 0.17936

= 0.82064

Therefore, the probability that a randomly chosen child has a height of more than 46.8 inches is 0.82064