Question

Suppose the taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. What is the probability that for 36 jets on a given runway total taxi and takeoff time will be

a) less than 6 minutes?

b) more than 9 minutes?

c) between 7.5 and 8.2 minutes

Answer 1

Solution :

Given that ,

mean = = 8.5

standard deviation = = 2.5

a)

P(x < 6) = P[(x - ) / < (6 - 8.5) / 2.5]

= P(z < -1)

= 0.1587

Probability = 0.1587

b)

P(x > 6) = 1 - P(x < 9)

= 1 - P[(x - ) / < (9 - 8.5) / 2.5)

= 1 - P(z < 0.2)

= 1 - 0.5793

= 0.4207

Probability = 0.4207

c)

P(7.5 < x < 8.2) = P[(7.5 - 8.5)/ 2.5) < (x - ) /  < (8.2 - 8.5) / 2.5) ]

= P(-0.4 < z < -0.12)

= P(z < -0.12) - P(z < -0.4)

= 0.4522 - 0.3446

= 0.1076

Probability = 0.1076