Help on binomial problems using minitab
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The document provides help on solving binomial probability problems using Minitab software. It explains how to calculate the probabilities of exactly 8 successes, at least 8 successes, and less than 8 successes when randomly sampling 10 men and the probability of any one man being a basketball fan is 49%. The key steps are to use Minitab's binomial distribution function, enter the number of trials (10), probability of success (0.49), and use the shaded area tab to calculate the probabilities by selecting the left, right, or middle tail as appropriate. The probabilities calculated are 0.03890 for exactly 8, 0.04800 for at least 8, and 0.9520 for less than 8.
Help on binomial problems using minitab
- 1. HELP ON BINOMIAL PROBLEMS B. Heard Not to be posted, shared or transmitted without my permission. Students may download one copy for their own personal use.
- 2. HELP ON BINOMIAL PROBLEMS One of my students was having trouble doing some of the binomial type problems and I decided to put this together knowing that at least a couple of other students might be having problems. I will look at a problem similar to number 4 in the Week 4 Homework.
- 3. HELP ON BINOMIAL PROBLEMS In the problem, it was known that a certain percentage of men were basketball fans, when the student asked, we were in the middle of the NCAA Tournament or “March Madness,” so it makes it even more appropriate (and fun). Let’s say that 49% of men are known to be basketball fans and we randomly select 10 men. Find the following probabilities. P(Exactly 8) P(At Least 8) P(Less Than 8)
- 4. HELP ON BINOMIAL PROBLEMS This screams “Binomial” and it is a very easy problem to solve with Minitab, if you understand the following 49% of men means p = 0.49 We randomly sampled 10 men, so n = 10 P(Exactly 8) means exactly 8 of the 10 P(At Least 8) means 8,9 or 10 P(Less Than 8) means 0,1,2,3,4,5,6, or 7 (DOES NOT INCLUDE 8)
- 5. HELP ON BINOMIAL PROBLEMS Go to Minitab, Up at the Top Graph >> Probability Distribution Plots Choose “View Probability” and Click OK Now Choose “Binomial” under Distribution Enter 10 as the Number of Trials Enter 0.49 as the Event Probability Then Click the Shaded Area Tab
- 6. HELP ON BINOMIAL PROBLEMS This is the Shaded Area Tab
- 7. HELP ON BINOMIAL PROBLEMS Now for P(Exactly 8) Click X Value, “Middle” and enter 8 as X Value 1 AND X Value 2, then Click OK
- 8. HELP ON BINOMIAL PROBLEMS Bazinga – P(Exactly 8) =0.03890 (Always round to the required number of decimals) You can use Middle to get “Exactly” Values By making the Value both X values 0.25 0.20 0.15 0.10 0.05 0.00 X Probability 8 0.03890 1 9 Distribution Plot Binomial, n=10, p=0.49
- 9. HELP ON BINOMIAL PROBLEMS Now for P(At Least 8) Click X Value, “Right Tail” and enter 8 as X Value and Click OK Why Right Tail? At least 8 means “8 or more” or “8 and to the right”
- 10. HELP ON BINOMIAL PROBLEMS Bazinga – P(At least 8) =0.04800 (Always round to the required number of decimals) 0.25 0.20 0.15 0.10 0.05 0.00 X Probability 8 0.04800 1 Distribution Plot Binomial, n=10, p=0.49
- 11. HELP ON BINOMIAL PROBLEMS Now for P(Less than 8) Click X Value, “Left Tail” and enter 7 as X Value and Click OK Why Left Tail? Less than 8 means “7 or less” or “7 and to the left” It doesn’t include the 8.
- 12. HELP ON BINOMIAL PROBLEMS Bazinga – P(Less than 8) =0.9520 (Always round to the required number of decimals) 0.25 0.20 0.15 0.10 0.05 0.00 X Probability 7 0.9520 9 Distribution Plot Binomial, n=10, p=0.49