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 55.6 inches, and standard deviation of 3.4 inches.

A) What is the probability that a randomly chosen child has a height of less than 57.7 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 47.2 inches?

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

Answer 1

SOLUTION:

From given data,

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.6 inches, and standard deviation of 3.4 inches.

We have,

Mean = = 55.6 inches

Standard deviation = = 3.4 inches

Let us consider X is Height of ten-year-old children's

X N ( , )

X N (55.6 , 3.4 )

Z = (X - ) / = (X - 55.6 ) / 3.4 ​​​​​​​

A) What is the probability that a randomly chosen child has a height of less than 57.7 inches?

P(X < 57.7) = P((X - ) / < (57.7 - 55.6 ) / 3.4 ​​​​​​​)

P(X < 57.7) = P( Z < 2.1 / 3.4 ​​​​​​​)

P(X < 57.7) = P( Z < 0.61 ​​​​​​​)

P(X < 57.7) = 0.72907

Answer = 0.729 (Round answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 47.2 inches?

P(X > 47.2) = P((X - ) / > (47.2 - 55.6 ) / 3.4 ​​​​​​​)

P(X > 47.2) = P(Z > - 8.4 / 3.4 ​​​​​​​)

P(X > 47.2) = P(Z > - 2.47 ​​​​​​​)

P(X > 47.2) = 1 - P(Z < - 2.47 ​​​​​​​)

P(X > 47.2) = 1 - 0.00676

P(X > 47.2) = 0.99324

Answer = 0.993  (Round your answer to 3 decimal places.)