Question

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 161 lb. The new population of pilots has normally distributed weights with a mean of 129 lb and a standard deviation of 29.1 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 120 lb and 161 lb. The probability is approximately _____. ​(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 120 lb and 161 lb. 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 sample of pilots 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 single pilot is more important.

Answer 1

Solution :

Given that ,

mean = = 129

standard deviation = = 29.1

a) P(120 < x < 161 ) = P[(120 - 129)/ 29.1) < (x - ) /  < (161 - 129) / 29.1 ) ]

= P(-0.31 < z < 1.10)

= P(z < 1.10 ) - P(z < -0.31)

Using z table,

= 0.8643 - 0.3783

= 0.4860

b) n = 37

=   = 129

= / n = 29.1 / 37 = 4.78

P(120 < < 161)  

= P[(120 - 129 ) / < ( - ) / < (161 - 129) / 4.78)]

= P(-1.88 < Z < 6.69)

= P(Z < 6.69) - P(Z < -1.88)

Using z table,  

= 1 - 0.0301   

= 0.9699

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