2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm), denoted by the random variable X, has the following probability distribution: 1 2 3 4 6 P(X=x) .05 .20 .25 .20 .10 .15 .05 a. Find the probability there will be 3 or more emergency room patients during a randomly selected 8-hour graveyard shift. b. Find the probability there will be an even number of patients. c. Find the probability there will be at least 2 but not more than 5 patients.

4.56 Nonstandard dice. Nonstandard dice can produce interesting distributions of outcomes. You have two balanced, six-sided dice. One is a standard die, with faces having one, two, three, four, five, and six spots. The other die has three faces with one spot and three faces with six spots. Find the probability distribution for the total number of spots Y on the up-faces when you roll these two dice.

For familiés with 5 children, let X be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable X? P(x) 1 0.2862 0.0776 3. 0.1155 4 0.0491 0.3974 O no O yes 2.

High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?

An electronics firm employs 15 people whose yearly salaries (in hundred thousands of pesos) are as follows: 25.0 25.7 25.7 26.6 27.2 27.3 27.3 27.3 27.3 27.8 27.8 28.4 28.4 29.0 29.0 a. Let X be the yearly salary for any employee. Find the probability distribution of X. b. Construct the probability histogram for the random variable X.

A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions re- quired to gain the patient's trust. The following probability function has been proposed. f(x) = for x = 1, 2, or 3 6. Is this probability function valid? Explain. b. What is the probability that it takes exactly two sessions to gain the patient's trust? с. What is the probability that it takes at least two sessions to gain the patient's trust?

British Travel Agency has asked a junior manager to investigate flight delays during the week before Christmas at Heathrow Airport. The random variable X is the number of flights delayed per hour. The results are shown in the following table. x 0 1 5 2 3 4 6 7 8. p(x) 0.10 0.08 0.07 0.15 0.12 0.08 0.10 0.12 0.08 0.10 a) Show that the probability distribution is well defined and derive the cumulative probability distribution. b) Find the probability that there would be three through seven (inclusive) delayed flights per hour? c) Find the mean and variance of flights delayed per hour.