Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between

120lb and 181lb. The new population of pilots has normally distributed weights with a mean of 126 lb and a standard deviation of 33.3lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 120lb and 181lb.The probability is approximately? ​(Round to four decimal places as​ needed.)

b. If 40 different pilots are randomly​ selected, find the probability that their mean weight is between

120lb and 181lb.The probability is approximately? ​(Round to four decimal places as​ needed.)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	126
std deviation   =σ=	33.300

probability =P(120<X<181)=P((120-126)/33.3)<Z<(181-126)/33.3)=P(-0.18<Z<1.65)=0.9505-0.4286=0.5219

b)

sample size       =n=	40
std error=σx̅=σ/√n=	5.27

probability =P(120<X<181)=P((120-126)/5.265)<Z<(181-126)/5.265)=P(-1.14<Z<10.45)=1-0.1271=0.8729