In the discussion forum for this week, you will create a scenario that requires the use of a binomial distribution. Before posting your problem, please review the criteria for a binomial distributions by reviewing Week 5 Binomial distribution and Binomial Distribution in Excel Week 5.
Instructions:
- For your post you will make up a problem that uses binomial distribution similar to the example below. Try to have 3 scenarios. You do not need to solve your own problem.
- If you can, try a probability different from .5. In your problem, make sure that the probability stays the same for each trial!
- You will answer problems from classmates for your responses. Copy the question and your Excel formulas into your forum posts so your professor and classmates can check your work. Then write a brief summary of the results after the problem you copied in your post.
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Example initial post:
For this example, assume that a family has 8 children, and the probability that any one child is a boy is .5.
a) Find the probability that the family has exactly 5 boys.
b) Find the probability that the family has more than 5 boys.
c) Find the probability that the family has at most 5 boys.
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For your response posts, here is how to solve these problems in Excel.
a) Find the probability that the family has exactly 5 boys.
Type into an Excel cell
=binom.dist(5,8,.5,False)
You should get .21875
b) Find the probability that the family has at most 5 boys.
Type into an Excel cell
=binom.dist(5,8,.5,True)
.855469 should be your answer
c) Find the probability that the family has more than 5 boys.
Type into an Excel cell:
=1-binom.dist(5,8,.5,True)
.144531 should be your answer
Notice that this answer is just 1 minus the answer from part b. Then, describe what these results mean by summarizing the results.
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Binomial in Excel Week 4.html
Week 5 – Example 4
Here is an example by the steps
Binomial Distribution
For 2007 and below use binomdist
For n=10 experiments
X=4
P=.6
Type in a cell
=binom.dist(4,10,.6, FALSE)
For n=10
X<=4
P=.6
type in an excel cell
=binom.dist(4,10,.6,TRUE)
For n=10
X<4
P=.6
type in a cell
=binom.dist(3,10,.6, TRUE)
For n=10
x>=4
type in a cell
=1-binom.dist(3,10,.6,TRUE)
,
Week 4 Binomial distribution illustrated by Bethany Mueller.html
Week 5 – Example 6
Here is an example by the steps
Binomial Distribution in Excel
For binomial distribution exercise, we use the binom.dist command in Excel.
(For Excel 2007 and older, use the command “binomdist.”)
Note: We use "true" if we're calculating a cumulative probability. We use "false" to calculate the exact probability. In a nutshell, type “TRUE” when you have a “less than” probability (like if the exercise has a strictly “<“ sign) and type “FALSE” when you have a strictly “equals” probability.
Example: A recent survey found that 17% of adults dislike Marshmallow Fluff. Suppose you randomly select four adults and ask them if they like Marshmallow Fluff.
- What is the probability that exactly two of them dislike Marshmallow Fluff?
- What is the probability that fewer than two of them dislike Marshmallow Fluff?
- What is the probability that at least two of them dislike Marshmallow Fluff?
- What is the probability that 2 or fewer dislike Marshmallow Fluff?
Part a: n = 4, P = 0.17 and x = 2 (we use x = 2 and "FALSE" because we're calculating the exact probability for "equals 2")
Part b: n = 4, P = 0.17 and x < 2 (“fewer than two” means zero or one so we use x = 1 and "TRUE" because we're adding the probabilities of 0 and 1)
Part c: n = 4, P = 0.17 and x >= 2 (“at least two” means two, three, or four; note that this is the compliment of part b)
Part d: n = 4, P = 0.17 and x <= 2 (“two or fewer” means zero, one or two so we use x = 2 and "TRUE" because we're adding the probabilities of 0, 1, and 2)
