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 probability that a flight is more than 140 minutes? B. What is the distribution's mean? C. What is the distribution's standard deviation? D. What is the probability that a flight is less than 135 minutes?

Question

Mathematics

Harmony Perez

15 July, 14:18

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 probability that a flight is more than 140 minutes? B. What is the distribution's mean? C. What is the distribution's standard deviation? D. What is the probability that a flight is less than 135 minutes?

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Answers (1)

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Emmy Swanson · Answer 1

a) 33.33%)

b) 135 minutes

c) 8.66 min

d) 50%

Step-by-step explanation:

a) the probability for a uniform distribution is

P (b
therefore the probability that the flight is more than 140 minutes (and less than 150 since it is the maximum value)

P (140
b) the mean (expected value) for a uniform probability distribution is

E (X) = (c+d) / 2 = (120+150) / 2 = 135 minutes

c) the standard deviation for a uniform probability distribution is

σ² (X) = (c-d) ²/12 = (150-120) ²/12 = 75 min²

σ = √75 min² = 8.66 min

b) following the same procedure as in a)

P (120