Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: xx  0 1 2 3 4 5 6 7 8 P(X=x)P(X=x)  0.207 0.136 0.328 0.18 0.091 0.036 0.017 0.003 0.002 What is the probability that a randomly selected student changed his or her major at least once?    What is the probability that a randomly selected student changed his or her major at most twice?    Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times?

A TV manufacturer receives LCD panels from a certain supplier. Let X denote the number of flaws in a randomly selected LCD panel from this supplier. Suppose that the probability distribution for X is:  X   0   1   2   3   4  probability   0.62     0.2     0.14     0.03     0.01   The mean value of X is  .

A deck of four (4) cards has exactly one (1) color printed on each face – blue, yellow, red, or green. You have two (2) identical decks of this type. In this game, you randomly select a card from each of the two decks. Your score is the number of blue cards drawn – refer to this quantity as X. The probability distribution is below: X P(X) 0 0.5625 1 0.375 2 0.0625 What is the probability that zero blue cards are drawn?

A small inn has 4 rooms.  Let X represent the number of rooms that are rented out on any given Saturday. The following table describes the probability distribution of X.     What is the mean of the random variable X?   μX =

Oxygen demand is a term biologists use to describe the oxygen needed by fish and other aquatic organisms for survival. The Environmental Protection Agency conducted a study of a wetland area. In this wetland environment, the mean oxygen demand was u = 9.3 mg/L with 95% of the data ranging from 6.7 mg/L to 11.9 mg/L. Let x be a random variable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. In USE SALT (a) Use the 95% data range to estimate the standard deviation for oxygen demand. (b) An oxygen demand below 8 indicates that some organisms in the wetland environment may be dying. What is the probability that the oxygen demand will fall below mg/L? (Round your answer to four decimal places.) (c) A high oxygen demand can also indicate trouble. An oxygen demand above 12 may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed…

Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15   Is this model a probability distribution? A. Yes. B. No. C. Maybe.

A deck of four (4) cards has exactly one (1) color printed on each face – blue, yellow, red, or green. You have two (2) identical decks of this type. In this game, you randomly select a card from each of the two decks. Your score is the number of blue cards drawn – refer to this quantity as X.  The probability distribution is below: X P(X) 0 0.5625 1 0.375 2 0.0625 What is the average number of blue cards drawn? What is the probability that at most one blue card is drawn?

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?

Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 1 2 3 5 6 7 8 P(X = x) 0.195 0.183 0.294 0.179 0.098 0.034 0.012 0.003 0.002 a. What is the probability that a randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. Given that a randomly selected person did change majors, what is the probability that he or she changed majors more than three times? Check Answer

A student who is taking a stats class was assigned to watch the cars driving along Pereira Drive and count the number of people who are in each cars. Let Y be the number of people in a given car that the student observe. The following table shows the cdf of Y: 1 3 4 P(Y < y) 0.06 0.32 0.71 0.88 1 (a) What is the probability that a given car has 2 people in it? (b) What is the probability that a give car has 3 or more people in it. (c) What is the expected number of people in a given car that the student observe.