Determine whether the distribution is a discrete probability distribution. 100 200 300 400 500 D P(x) 0.22 0.28 0.13 0.18 0.23 Is the distribution a discrete probability distribution? A. No, because the sum of the probabilities is not equal to 1. B. Yes, because the sum of the probabilities is equal to 1. C. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive. D. No, because each probability is not between 0 and 1, inclusive.

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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?

Determine whether the table gives the probability distribution of the random variable X. Explain your answer. x −1 0 1 2 3 P(X = x) 0.3 0.1 0.2 0.2 0.2 A. Yes, because the probabilities are all between 0 and 1, inclusive, and the values are all unique. B. Yes, because the sum of the probabilities is equal to 1 and the values are all unique.     C. Yes, because the probabilities are all between 0 and 1, inclusive, and their sum is equal to D. No, because the sum of the probabilities is not less than 1. E. There is not enough information to tell.

Determine whether the distribution is a discrete probability distribution. P(x) 0.25 1 0.30 2 - 0.10 3 0.30 4 0.25 Is the distribution a discrete probability distribution? Why? Choose the correct answer below. O A. Yes, because the probabilities sum to 1 and are all between 0 and 1, inclusive. B. Yes, because the distribution is sym tric. C. No, because some of the probabilities have values greater than 1 or less than 0. D. No, because the total probability is not equal to 1.

Determine the required value of the missing probability to make the distribution a discrete probability distribution. X P(x) - 3 0.22 4 ? 0.53 6. 0.06 ..... P(4) = (Type an integer or a decimal.)

Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(x) - 0.22 4 ? 0.46 6. 0.16 ... P(4) = (Type an integer or a decimal.)

Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(x) 3 0.33 4 ? 0.22 0.22 P(4) = (Type an integer or a decimal.)

Hour: 1. Let Y the number of siblings for a student at a local high school. Suppose we choose someone from the school at random. The probability distribution of Y is as Name: Date: follows. Y 2. 3. 4 5+ Probability 0.02 0.25 0.35 0.20 0.10 0.08 (a) Is Y a discrete or continuous? Explain. (b) Is this a valid probability distribution? Explain. (c) Create a histogram for the probability distribution and describe its shape. (d) Find the probability that the randomly selected student has at least one sibling. (e) Describe in words what P(Y>2) means and find the probability. (f) Calculate the mean of Y. Interpret this in context. (g) The standard deviation is 1.236. Interpret this in context. © 2017 BFW Publishers Starnes/Tabor Statistics and Probability with Applications 3/e

Determine the required value of the missing probability to make the distribution a discrete probability distribution. P(4) = (Type an integer or a decimal.) ... X 3 4 5 6 P(x) 0.35 ? 0.38 0.12