Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 157 lb and a standard deviation of 29.1 lb. a. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 191 lb. The probability is approximately nothing. ​(Round to four decimal places as​ needed.) b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 191 lb. The probability is approximately nothing. ​(Round to four decimal places as​ needed.) c. When redesigning the ejection​ seat, which probability is more​ relevant? A. Part​ (b) because the seat performance for a single pilot is more important. B. Part​ (a) because the seat performance for a sample of pilots is more important. C. Part​ (b) because the seat performance for a sample of pilots is more important. D. Part​ (a) because the seat performance for a single pilot is more important.

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	157
std deviation   =σ=	29.100

  probability that his weight is between 150 lb and 191 lb:

probability =

P(150<X<191)

=

P(-0.24<Z<1.17)=

0.8790-0.4052=

0.4738

b)

sample size       =n=	37
std error=σx̅=σ/√n=	4.7840

probability that their mean weight is between 150 lb and 191 lb:

probability =

P(150<X<191)

=

P(-1.46<Z<7.11)=

1-0.0721=

0.9279

c)

  Part​ (a) because the seat performance for a single pilot is more important.