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BMA4003 – Managing Data

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BMA4003 – Managing Data

Assessed Seminar 1

Uniform and Normal Probability Distribution.

Activity 1: Normal Distribution

Airfares were based on the total ticket value, which consisted of the price charged by the airlines plus any additional taxes and fees. Please, use the Excel file titled “Assessed Seminar 1 – Data”.

  1. The prices follow normal distribution. Use Excel to plot the density of the prices.

You can either use pen and paper or Excel for question 2-5. Please use the z score formula to calculate the question 2-5.

  • What is the probability that a domestic airfare is $525 or more?
  • What is the probability that a domestic airfare is $225 or less?
  • What if the probability that a domestic airfare is between $350 and $450?
  • What is the cost for the 4% highest domestic airfares?
  • Use Excel functions Norm.Dist and Norm.INV to check your answers in Question 2-5.
  • What is the 95% confidence interval for a sample containing 100 values?

Activity 2: Uniform probability distribution

Delta Airlines quotes a flight time of 2 hours, 10 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 30 minutes.

  1. Give a mathematical expression for the probability density function of flight time and the expected value and variance of the distribution.
  • Create a scatter graph using dynamic process learnt in the previous sessions to show the uniform probability distribution graphically, then answer the below questions:
  1. What is the probability that the flight will be no more than 5 minutes late?
    1. What is the probability that the flight will be more than 10 minutes late?
    1. What is the probability that the flight will be between 6 and 10 minutes late?
    1. In a month of 250 flight journeys finished, how many should have arrived 3 minutes or less earlier?

End of Seminar 1