Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 130 lb and a standard deviation of 33.7lb.

a. If a pilot is randomly selected, find the probability that his weight is between 120 lb and 171 lb.

The probability is approximately __. (Round to four decimal places as needed.)

b. If 32 different pilots are randomly selected, find the probability that their mean weight is between 120 lb and 171lb.

The probability is approximately __. (Round to four decimal places as needed.

c. When redesigning the ejection seat, which probability is more relevant?

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

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

C. Part (a) because the seat performance for a sample of pilots is more important.

D. Part (b) because the seat performance for a sample of pilots is more important.

Answer 1

Solution :

Given that,

mean = = 130

standard deviation = = 33.7

a ) P (120 < x < 171 )

P ( 120 - 130 / 33.7) < ( x -  / ) < ( 171 - 130 / 33.7)

P ( - 10 / 33.7 < z < 41 / 33.7 )

P (-0.30 < z < 1.22)

P ( z < 1.22 ) - P ( z < - 0.30)

Using z table

= 0.8888 - 0.3821

= 0.5067

Probability = 0.5067

b ) n = 32

= 130

₌ / n = 33.7 32 = 5.9574

P (120 < < 171 )

P ( 120 - 130 / 5.9574) < ( -  / ) < ( 171 - 130 /5.9574)

P ( - 10 / 5.9574 < z < 41 / 5.9574 )

P (-0.30 < z < 6.88)

P ( z < 6.88 ) - P ( z < - 1.68)

Using z table

= 1 - 0.0465

= 0.9535

Probability = 0.9535

c ) Option D ) is correct. D. Part (b) because the seat performance for a sample of pilots is more important.