 # 1. Describe how each of these three questions refers to a binomial ...

## Question

1. Describe how each of these three questions refers to a binomial probability distribution. Determine and explain your answer to each of the three questions. Include the Excel output in your submission.
a. You have invited 10 friends to a cookout. On any given day, the probability that any one of them will elect to eat a hotdog as their entrée is 35%. You have 4 hotdogs. What is the likelihood that you will run out of hotdogs?
b. The weather forecast says that there is a 20% chance of rain each of the 4 hours during which your picnic is scheduled. What is the probability that there will be no rain in 3 of the 4 hours?
c. As you play softball, you know that each of your guests reaches base 40% of the time. What is the likelihood that in their first time at bat, exactly 6 of 10 of your guests will reach base?

2. Select one of menu preference, weather forecasts, or batting average and describe how the binomial probability distribution could be used to aid a commercial business.

## Solution Preview

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Problem 1 a)

You have invited 10 friends to a cookout. On any given day, the probability that any one of them will elect to eat a hotdog as their entrée is 35%. You have 4 hotdogs. What is the likelihood that you will run out of hotdogs?

Solution:
This is a problem about the binomial distribution.
N= number of trials =10 is the number of participants.
X is the number of successes = number of hotdogs eaten,
and the probability that anyone of the participants eats a hot dog is equal to p = 0.35. We assume that whether anyone eats a hotdog is independent of whether anyone else chooses to eat a hotdog, and that anyone eats at most one hotdog.

We run out of hotdogs when X>4 and so we need to determine the probability P(X>4).
Since X has the binomial distribution: P(X=k)= 10Ck pk(1-p)(10-k) _, with p=0.35.

In Excel we can compute the probability that P(X<=4) as: binom.dist(4,10,0.35,TRUE) and we obtain P(X<=4)= 0.751496. Therefore P(X>4)=1-P(X<=4)= 0.248504, which is then the probability that we run out of hotdogs....

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