You are allowed to use Excel’s built-in functions to complete the following exercises, such as “BINOMDIST”. Be sure to show and clearly label each logical step taken to complete each problem.
Major software manufacturers offer a help line that allows customers to call and receive assistance in solving their problems. However, because of the volume of calls, customers are frequently put on hold. One software manufacturer claims that only 20 % of callers are put on hold. Suppose that 100 customers call. What is the probability that more than 25 of them are put on hold?
According to the Gallup poll conducted March 5-7, 2001, 52% of American adults think that protecting the environment should be given priority over developing the U.S. energy supplies. 36% think that developing energy supplies is more important, and 6% believe the two are equally as important. The rest (6%) had no opinion. Suppose that a sample of 100 American adults is quizzed on the subject. What is the probability of the following events?
A. 50 or more think that protecting the environment should be given priority.
B. Thirty or fewer think that developing energy supplies is more important.
C. 5 or fewer have no opinion.
Use the “Random Number Generation” feature of Excel’s Data Analysis ToolPak to complete the following exercises. You may also use Excel’s built-in functions such as “AVERAGE” and “VAR.P” to complete them.
L3.1 Let X represent the number of Heads observed after flipping a fair coin 10 times. In this exercise you will simulate flipping a fair coin 10 times, recording the number of Heads observed, and then repeating the experiment 1,000 times. In other words, you will generate 1,000 observations for X.
a. Open the Random Number Generation dialogue box and select “Binomial” for “Distribution”.
i. Enter “1” for “Number of Variables” and “1000” for “Number of Random Numbers”.
ii. Enter “0.5” for “p Value” and “10” for “Number of trials”.
iii. Under “Output options”, select “Output Range” and click on the cell where you want the data to begin populating. When finished, you should see a column of 1,000 randomly-generated values of X
b. Based on your data, what are the Mean and Variance of X? Are those values consistent with the theoretical mean and variance of a binomially-distributed random variable? (If you simply answer “Yes” or “No” to this question, Dr. Steimetz will drop you from the class and then change your major to “Undeclared”.)
c. Using your data, construct a Probability Distribution table for X (i.e. a relative frequency table).
d. Using that table, create a Bar Chart showing the relative frequency of values for X ranging from zero to ten. Briefly comment on the shape of this histogram.
Notes on Creating Bar Charts in Excel
1. What we call a “Bar Chart” in class, Excel calls a “Column” chart.
2. By default, Excel labels the X-axis as 1, 2, 3, and so forth. If you want the values on the X-axis to match the values in your relative frequency table:
a. First create your bar chart with Excel’s default labeling.
b. Right-click on a blank area of your chart and click on “Select Data”.
c. Under “Horizontal (Category) Axis Labels”, click on “Edit”.
d. Select the cells that contain your values of X and then click “Ok”.