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 6 inches.

A) What is the probability that a randomly chosen child has a height of less than 65 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 55.2 inches?

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

Answer 1

Normal distribution: P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 53.5 inches

Standard deviation = 6 inches

A) P( height of less than 65 inches) = P(X < 65)

= P(Z < (65 - 53.5)/6)

= P(Z < 1.92)                               (z score rounded to 2 decimal places)

= 0.9726

= 0.973                                       (final answer rounded to three decimal places)

B) P(height of more than 55.2 inches) = P(X > 55.2)

= 1 - P(X < 55.2)

= 1 - P(Z < (55.2 - 53.5)/6)

= 1 - P(Z < 0.28)                               (z score rounded to 2 decimal places)

= 1 - 0.6103

= 0.3897

= 0.390                                            (final answer rounded to three decimal places)