Question

1)

The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches.

Assume that such an individual is selected at random. What is the probability that his height will be greater than 67.8 inches?

Round your answer to 4 decimal places.

Answer 1

Solution:

Given, the Normal distribution with,

   = 69.3

= 2.8

Find P( height will be greater than 67.8 inches) i.e. P(X > 67.8)

P(X > 67.8) = P[(X - )/ >  (67.8 - )/]

= P[Z > (67.8 - 69.3)/2.8]

= P[Z > -0.5357]

= 1 - P[Z < -0.5357]

=    1 - 0.2961 ( use z table or calculator)

=    0.7039