In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows the results obtained (Gallup website, August 6, 2012).

  Number of Cups                      Number of

         per Day                                Responses

              0 …………………………............…  365

              1 …………………………............…  264

              2 ………………………............……  193

              3 ………………………...........……     91

              4 or more ………….....………     101

Define a random variable x 5 number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.

a. Develop a probability distribution for x.

b. Compute the expected value of x.

c. Compute the variance of x.

d. Suppose we are only interested in adults who drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y and compare it to the expected value of x.