Question

In the country of United States of Height, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53.1 inches, and standard deviation of 3.8 inches.
What is the probability that the height of a randomly chosen child is between 45.1 and 53.5 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Answer=
(Round your answer to 3 decimal places

Answer 1

Answer:

a) We need to find p(x<68.15)

Standardize x to z, we have, z = (68.15-μ)/σ

=(68.15-57)/8.1

=1.38

Reading from standard normal tables,

p(z<1.38) =0.9162.

b) We need to find p(x>54.4)

Standardize x to z, we have, z = (54.4-μ)/σ

=(54.4-57)/8.1

=-0.32

Reading from standard normal tables,

p(z>-0.32) = 0.6255