Question

________I. Which of the following is an example of a discrete random variable?

1. The weight of a box of cookies
2. The length of a window frame
3. The number of houses in a development
4. The distance from home to school

________II. The following table shows the population probability distribution of x, the random variable representing the price per ticket, in dollars, for 20 upcoming concerts at a certain community’s civic center.

          Price per ticket ($)                          P(x)

                                45                                           0.20

                                48                                           0.20

                                50                                           0.15

                                53                                           ?

                                55                                           0.25

How many of the 20 concerts will cost $53 per ticket?

1. 2      B)   3      C)   4      D)   5

________III. Which of the following is an example of a binomial experiment?

1. Rolling a die 10 times and recording the number of times all six possible outcomes occur
2. Selecting five persons and asking whether they are in favor of an issue, against, it or have no opinion
3. Tossing a coin 20 times and counting the number of heads that occur
4. Drawing three marbles from a box that contains red, blue, and yellow marbles

Answer 1

I The following is an example of a discrete random variable:-

C. The number of houses in a development

It can only be a whole number, hence discrete

II

c)4

Now P(X=53) = 1 - (0.20+0.20+0.15+0.25) = 1 - 0.8 = 0.20

Therefore out of 20 concerts, 20% * 20 = 4 will cost $53 per ticket.

III

c) Tossing a coin 20 times and counting the number of heads that occur

The above satisfies all conditions for a binomial experiment.

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