Determine whether the distribution is a probability distribution.  If it is not a probability distribution, explain why. The random variable x represents the number of classes in which a student is enrolled in a given semester at a university.  x 1 2 3 4 5 6 7 8 P(x) 1 /80 2 /75 1 /10 12/ 25 27 /20 1 /5 2 /25 1/120

Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the probability distribution of x is given in the table shown below. 95 96 97 98 99 100 101 102 P(x) 0.06 0.09 0.12 0.14 0.23 0.15 0.07 0.05 103 104 105 106 107 108 109 110 p(x) 0.04 0.02 0.01 0.005 0.005 0.005 0.0031 0.0019 (a) What is the probability that the airline can accommodate everyone who shows up for the flight? (b) What is the probability that not all passengers can be accommodated? (c) If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight? What if you are number 3?

The probability distribution below is for the random variable X = the number of credits taken by a randomly selected first-year student at a large state university. Credits 14 15 16 17 Probability 0.05 0.65 0.20 0. 10 Show that the probability distribution of X is valid.

You roll a fair, four-sided die twice. Let the random variable X = "number of times rolled on the number 4," with x = 0, 1, 2.Which histogram shows the correct probability distribution based on the scenario above? (choose one of three graphs in image)