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 53.7 inches, and standard deviation of 2.2 inches.

What is the probability that the height of a randomly chosen child is between 48.4 and 49.7 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Answer 1

Solution :

Given that,

mean = = 53.7

standard deviation = = 15

P (48.4 < x < 49.7 )

P ( 48.4 - 53.7 / 2.2 ) < ( x -  / ) < ( 49.7 - 53.7 / 2.2 )

P ( -5.3 / 2.2 < z < -4 / 2.2 )

P (-2.41 < z < -1.82 )

P ( z < -1.82 ) - P ( z < -2.41)

Using z table

= 0.0344 - 0.0080

= 0.0264

Probability = 0.0264