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.

1. HELP ON BINOMIAL
PROBLEMS
B. Heard
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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