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 53.6 inches, and standard deviation of 6.9 inches. A) What is the probability that a randomly chosen child has a height of less than 56.55 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 62.4 inches? Answer= (Round your answer to 3 decimal places.)

Answer 1

A) Given data

Height measurements are uniformity distributed with

Mean Value (X')=53.6

Standard deviation (S)=6.9

We need to determine the probability for the following two cases

A) The probability that a randomly choosen child has a height of less than 56.55 inches is

I.e P(X<56.55)

First determine the z score Value

Z score=(X-X')/S

=(56.55-53.6)/6.9

=0.4275

P(X<56.55)=P(Z<0.4275)

=P(Z<0.43)

=0.6664 (From normal area tables)

B)The probability that a randomly choosen child has a height of more than 62.4 is

Z score=(X-X')/S

=(62.4-53.6)/6.9

=1.275

P(X>62.4)=P(Z>1.275)

=P(Z>1.28)

=0.1003 (From normal area tables)