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 56.5 inches, and standard deviation of 2.6 inches. What is the probability that the height of a randomly chosen child is between 53.6 and 57.8 inches?

Do not round until you get your your final answer, and then round to 3 decimal places.

Answer 1

Solution :

Given that ,

mean = = 56.5

standard deviation = = 2.6

P(53.6 < x < 57.8 ) = P[(53.6 -56.5) / 2.6 < (x - ) / < (56.5-57.8 ) / 2.6 )]

= P( -1.12< Z <-0.5 )

= P(Z < -0.5) - P(Z <-1.12 )

Using z table   

=0.3085 -0.1314

probability= 0.1771