Question

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes.
A) What is the distribution's mean?
B) What is the distribution's standard deviation?
C) What is the probability that a flight is less than 135 minutes?
D) What is the probability that a flight is more than 140 minutes?

Answer 1

Answer:

a) 135 minutes

b) 15

c) 0.5

d) 0.3707

Step-by-step explanation:

A) What is the distribution's mean

mean(m) = (120 + 150)/2 = 270/2 = 135 minutes

B) What is the distribution's standard deviation

standard deviation(s) $= \sqrt{\frac{(120-135)^{2}+(150-135)^{2} }{2} }$

s = 15

C) What is the probability that a flight is less than 135 minutes

firstly calculate z score

z score = (x - m)/s = (135 - 135)/15 = 0

P(x<135) = z(0) = 0.5

D) What is the probability that a flight is more than 140 minutes?

z score = (x - m)/s = (140 - 135)/15 = 0.33

P(x>140) = 1 - P(x<140) = 1 - 0.6293 = 0.3707