THE BINOMIAL PROBABILITY DISTRIBUTION
The binomial probability distribution is a discrete probability distribution controlled by the number of trials, n, and the probability of success on a single trial, p. The Excel function that generates binomial probabilities is BINOM.DIST(r,n,p,cumulative)
where r represents the number of successes. Using TRUE for cumulative returns the cumulative probability of obtaining no more than r successes in n trials, and using FALSE returns the probability of obtaining exactly r successes in n trials.
You can type the command directly in the formula bar (don't forget the preceding equal sign), or you can call up the dialog box by pressing the Insert Function (Function Wizard) button on the menu bar, then selecting Statistical in the drop down box and BINOM.DIST.
To compute the probability of exactly three successes out of four trials where the probability of success on a single trial is 0.50, we would enter the following information into the dialog box. When we press Enter, the formula result 0.25 will appear in the active cell.
LAB ACTIVITIES FOR BINOMIAL PROBABILITY DISTRIBUTIONS
1. You toss a coin n times. Call heads success. If the coin is fair, the probability of success p is 0.5. Use BINOM.DIST command with False for cumulative to find each of the following probabilities.
(a) Find the probability of getting exactly five heads out of eight tosses.
(b) Find the probability of getting exactly twenty heads out of 100 tosses.
(c) Find the probability of getting exactly forty heads out of 100 tosses.
2. You toss a coin n times. Call heads success. If the coin is fair, the probability of success p is 0.5. Use BINOM.DIST command with True for cumulative to find each of the following probabilities
(a) Find the probability of getting at least five heads out of eight tosses.
(b) Find the probability of getting at least twenty heads out of 100 tosses.
(c) Find the probability of getting at least forty heads out of 100 tosses.
Hint: Keep in mind how BINOM.DIST works. Which should be larger, the value in (b) or the value in (c)?
3. A bank examiner's record shows that the probability of an error in a statement for a checking account at Trust Us Bank is 0.03. The bank statements are sent monthly. What is the probability that exactly two of the next twelve monthly statements for our account will be in error? Now use the BINOM.DIST with True for cumulative to find the probability that at least two of the next twelve statements contain errors. Use this result with subtraction to find the probability that more than two of the next twelve statements contain errors. You can activate a cell and use the formula bar to do the required subtraction.
4. Some tables for the binomial distribution give values only up to 0.5 for the probability of success p. There is a symmetry between values of p greater than 0.5 and values of p less than 0.5.
(a) Consider the binomial distribution with n = 10 and p = .75. Since there are anywhere from 0 to 10 successes possible, put the numbers 0 through 10 in Cells A2 through A12. Use Cell A1 for the label r. Use BINOM.DIST with cumulative False option to generate the probabilities for r = 0 through 10.
Store the results in Cells B2 through B12. Use Cell B1 for the label p = 0.75.
(b) Now consider the binomial distribution with n = 10 and p = .25. Use BINOM.DIST with cumulative False option to generate the probabilities for r = 0 through 10. Store the results in Cells C2 through C12. Use Cell C1 for the label p = 0.25.
(c) Now compare the entries in Columns B and C. How does P(r = 4 successes with p = .75) compare to P(r = 6 successes with p = .25)?
5. (a) Consider a binomial distribution with fifteen trials and probability of success on a single trial p = 0.25. Create a worksheet showing values of r and corresponding binomial probabilities. Generate a bar graph of the distribution.
(b) Consider a binomial distribution with fifteen trials and probability of success on a single trial p = 0.75. Create a worksheet showing values of r and the corresponding binomial probabilities. Generate a bar graph.
(c) Compare the graphs of parts (a) and (b). How are they skewed? Is one symmetric with the other?
Attachment:- Assignment File.rar