Question

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.6 minutes and a standard deviation of 3 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. 

(a) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) 

(b) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) 

(c) What is the probability that for 33 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

Answer 1

S= X1+ X2+ ...+ Xn

here n = 33, mu = 8.6 ,sigma = 3

hence

S = N(33 * 8.6 , 33* 3^2)

= N( 283.8 , 297)

Z = (S - 283.8)/17.233687

normal
mean	283.8
sd	17.23368794
			p
below		320	0.9822
above		275	0.6952
between	275	320	0.6774