Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 157 lb and a standard deviation of 29.7 lb.
a. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 201 lb.

Answer 1

Solution :

Given that,

mean = = 157

standard deviation = = 29.7

P (150 < x < 201 )

P ( 150 - 157 / 29.7) < ( x -  / ) < ( 201 - 157 / 29.7)

P ( - 7 / 29.7 < z < 44 / 29.7 )

P (-0.23 < z < 1.48 )

P ( z < 1.48 ) - P ( z < -0.23)

Using z table

= 0.9306 - 0.4090

= 0.5216

Probability = 0.5216