Question

Delta airlines quotes a flight time of 2 hours, 5 minutes for its flight from Cincinnati to Tampa. Assume that the probability of a flight time within any one-minute interval is the same as the flight time within any other one-minute interval contained within the larger interval, 120 and 140 minutes.

*State the objective: What is the probability that the flight will be no more than 5 minutes late?

•Q1: What pdf best describes (models) the situation or assigns probabilities to outcomes of r.v.?

•Q2: Name and given values for parameters in the pdf.

•Q3: Define r. v.?

•Q4: Is r.v. discrete or continuous? (Make sure consistent with Q1)

•Q5: Write down the objective, question, or problem statement and then translate the English version into a statistics problem (using statistical and math language/formulas)

•Q6: Solve the objective.

Answer 1

•Q1: What pdf best describes (models) the situation or assigns probabilities to outcomes of r.v.?

Here the distribution is uniform distribution where the time varies between 120 minutes to 140 minutes

•Q2: Name and given values for parameters in the pdf.

Here parameters of the distribution is upper limit = b = 140 mins

Lower limit = 120 mins

•Q3: Define r. v.?

Here r.v. is the time taken by flight.

•Q4: Is r.v. discrete or continuous? (Make sure consistent with Q1)

It is continous.

•Q5: Write down the objective, question, or problem statement and then translate the English version into a statistics problem (using statistical and math language/formulas)

Here objective is to find probability that the flight will be no more than 5 minutes late.

Where question is find that how much would be the flight time that flight would be no more than 5 minutes late that means the flight time shall be less than 120 + 10 = 130 mins. Here as the distribution is uniform so we would calculate the value where x is less than 130 mins

•Q6: Solve the objective.

Pr(x < 130 mins) = (130 - 120)/(140 - 120) = 10/20 = 0.5