Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 135 lb and a standard deviation of 34.5 lb.

Answer 1

Solution :

Given that ,

mean = = 135

standard deviation = = 34.5

P(130 < x < 191) = P((130-135)/34.5 ) < (x - ) /  < (191-135) / 34.5) )

= P(-0.145 < z <1.623 )

= P(z <1.623 ) - P(z <-0.145 )

= 0.9477 - 0.4424

= 0.5053

The seat was designed for pilots weighing between 130 lb and 191 lb.is 0.5053