Airlines typically accept more reservations for a flight than the number of seats on the plane. Suppose that for a certain route, an airline accepts 40 reservations on a plane that carries 38 passengers. Based on experience, the probability distribution of Y = the number of passengers who actually show up for a randomly selected flight is given in the following table. You can check that μY = 37.4 and σY = 1.24.

There is also a crew of two flight attendants and two pilots on each flight. Let X = the total number of people (passengers plus crew) on a randomly selected flight.

a. Make a graph of the probability distribution of X. Describe its shape.

b. Find and interpret μX .

c. Calculate and interpret σX .

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Number of passengers yi 35 36 37 38 39 40 Probability p; 0.10 0.10 0.30 0.35 0.10 0.05