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 53.4 inches, and standard deviation of 6.4 inches.

A) What is the probability that a randomly chosen child has a height of less than 51 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 38.7 inches?

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

Answer 1

Solution :

Given that,

mean = = 53.4

standard deviation = = 6.4

P(X<51 ) = P[(X- ) / < (51 - 53.4) / 6.4]

= P(z < -0.38)

Using z table

probability = 0.352

b

P(X>38.7 ) = 1 - P[(X- ) / < (38.7 - 53.4) / 6.4]

= 1 - P(z < -2.30)

Using z table

=1 -0.0107

probability = 0.989