Question

I need answers for QUESTION 1 , 2 AND 3!

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 155 lb and a standard deviation of 33.6 lb.

A. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 201 lb.

Question #1 Part A: The probability is approximately ________?  ​(Round to four decimal places as​ needed.)

B. If 30 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 201 lb.

Question #2 Part B: The probability is approximately _____? ​(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 single pilot 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 sample of pilots is more important.

Answer 1

Solution :

Given that ,

mean = = 155 lb

standard deviation = = 33.6 lb

A) P(150 < x < 201) = P[(150 - 155)/ 33.6) < (x - ) /  < (201 - 155) / 33.6 ) ]

= P(-0.15 < z < 1.37)

= P(z < 1.37) - P(z < -0.15)

Using z table,

= 0.9147 - 0.4404

= 0.4743

B) n = 30

= = 155 lb

= / n = 33.6 / 30 = 6.13

P(150 < < 201)  

= P[(150 - 155) /6.13 < ( - ) / < (201 - 155) / 6.13)]

= P(-0.82 < Z < 7.50)

= P(Z < 7.50) - P(Z < -0.82)

Using z table,  

= 1 - 0.2061

= 0.7939

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