Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 140 lb and a standard deviation of 34.9 lb.

a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately

b. if number different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 171 lb.

The probability is approximately

c. when redesigning the ejection seat, which probability is more relevent ? part A or Part B

Answer #1

a.)

We Know ,

X follows N( 140, 34.92)

Z = (X-)/

therefore

P(130<X<171)=P( -.2865<Z<.8882)

= P(Z<.8882)-P(Z<=-.2865)

=P(Z<.8882)-(1-P(Z<-.2865)) [ P(Z<=-z)=P(Z>=z) ]

=.81257-(1-.61226)

=.42483 or 42.483% ( this is an approximate probability)

b.)

please let me know the the random sample size n of part b

(xbar-mu)/(sigma/) follows N( 0,1) ( Standard Normal)

the probability can be solved further using standard normal probabilities

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