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 54.8 inches, and standard deviation of 7.7 inches. A) What is the probability that a randomly chosen child has a height of less than 63.15 inches? B) What is the probability that a randomly chosen child has a height of more than 50.3 inches?

Answer 1

Solution :

Given that ,

mean = = 54.8

standard deviation = = 7.7

A)

P(x < 63.15) = P((x - ) / < (63.15 - 54.8) / 7.7)

= P(z < 1.08)

= 0.8599 using standard normal table.

Probability = 0.8599

B)

P(x > 50.3) = 1 - P(x < 50.3)

= 1 - P((x - ) / < (50.3 - 54.8) / 7.7)

= 1 - P(z < -0.58)

= 1 - 0.2810   

= 0.7190

Probability = 0.7190