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 55.8 inches, and standard deviation of 5.4 inches. A) What is the probability that a randomly chosen child has a height of less than 60.1 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 50.8 inches? Answer= (Round your answer to 3 decimal places.)

Answer 1

Solution :

Given, X follows Normal distribution with,

   = 55.8

   = 5.4

A) Find P(X < 60.1)

P(X < 60.1)

= P[(X - )/ <  (60.1 - )/]

= P[Z <  (60.1 - 55.8)/5.4]

= P[Z < 0.796]

= 0.7870 ... ( use z table)

P(X < 60.1) = 0.787

B)  Find P(X > 50.8)

= P[(X - )/ >  (50.8 - )/]

= P[Z > (50.8 - 55.8)/5.4]

= P[Z > -0.926]

= 1 - P[Z < -0.926]

= 1 - 0.1772     ( use z table)

= 0.8228

P(X > 50.8) = 0.823