Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 181 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 27.3 lb. If a pilot is randomly​ selected, find the probability that his weight is between 130 lb and 181 lb.

Answer 1

Solution :

Given that ,

mean = = 140 lb

standard deviation = = 27.3 lb

P(130 < x < 181 ) = P[(130 - 140 )/ 27.3 ) < (x - ) /  < (181 - 140 ) / 27.3 ) ]

= P( -01.87 < z < 1.50 )

= P(z < 1.50 ) - P(z < -1.87 )

Using z table

= 0.9332 - 0.0307

= 0.9025

The probability is = 0.9025