Question

an engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130 lb abd 181 lb. the new population of pilots has normally distributed weights with a mean of 128 lb and a stadard deviation of 27.9 lb

a) if a pilot is randomly selected, find the probability that his weight is between 130 lb and 181 lb

b) if 30 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 181 lb

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	128
std deviation   =σ=	27.900

a)

probability =P(130<X<181)=P((130-128)/27.9)<Z<(181-128)/27.9)=P(0.07<Z<1.9)=0.9713-0.5279=0.4434

b)

sample size       =n=	30
std error=σx̅=σ/√n=	5.09

probability =P(130<X<181)=P((130-128)/5.094)<Z<(181-128)/5.094)=P(0.39<Z<10.4)=1-0.6517=0.3483