University of London Binomial Distribution Questions
1. Give a real-world example of a distribution of data (a discrete random variable) that would be considered binomial.
Explain how your example might satisfy each condition.
1a) In your example, what is a trial? (Remember the trial is the action that is repeated)
1b) In your example, what would make a trial a success? What would make a trial a failure?
The next two are not always easy to determine, but give it your best shot
1c) In your example, does the result (success or failure) of any trial depend on the results of any of the previous trails?
1d) In your example, does each trial have the same probability of coming out as success?
2. Solve the following problem:
About 30% of adults in United States have a college degree. (The probability that a person has college degree is p = 0.30).
For N, choose any positive whole number from 35 to 45. For X, choose any positive whole number that is not greater than your choice of N.
State your choice of numbers: N=___ X=___
If N adults are randomly selected, find the probability of each of the following:
2a) Exactly X out of selected N adults have college degree
2b) Fewer than X out of selected N adults have college degree
2c) More than X out of selected N adults have college degree
2d) With each probability that you compute, give an interpretation in the context of the problem using %.
Here’s an example of an interpretation in context, with N = 25 and X = 7:
We have P(X = 7) = 0.121853726, so we can then say:
Each time we randomly select 25 adults, we expect about 12% of our selections to contain exactly 7 adults with a college degree.