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 caps per day Number of Responses 0 365 1 264 2 193 3 91 4 or more 101 Define a random variable x = 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.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 caps per day | Number of Responses |
| 0 | 365 |
| 1 | 264 |
| 2 | 193 |
| 3 | 91 |
| 4 or more | 101 |
Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups.
a. Develop a
b. Compute the
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.
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