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 56.4 inches, and standard deviation of 6.5 inches.

A) What is the probability that a randomly chosen child has a height of less than 63.95 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 72.8 inches?

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

Answer 1

Solution :

Given that ,

mean = = 56.4

standard deviation = = 6.5

Solution :

Given that ,

mean = = 56.4

standard deviation = = 6.5

P(X <63.95 ) = P(x <72.8)

= P((x - ) / < (63.95- 56.4 ) / 6.5)

= P(z <1.16 )   Using standard normal table,

= 0.8770

  Probability = 0.8770

(b)P(X >72.8 ) = 1 - P(x <72.8)

= 1 - P((x - ) / < (72.8 - 56.4 ) / 6.5)

= 1 - P(z <2.52 )   Using standard normal table,

= 1 - 0.9941   

= 0.0059

P(x >72.8 ) = 0.0059

Probability = 0.0059