University of California Characteristics of A Binomial Random Variable Questions Recall that the characteristics of a binomial random variable are:

1. The experiment consists of a fixed number (we usually use n) of trials.

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University of California Characteristics of A Binomial Random Variable Questions Recall that the characteristics of a binomial random variable are:
1. The

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2. The trials are independent.

3. There are only two possible outcomes on each trial, which for convenience we call success and failure.

4. The probability of a success (p), is the same for each observation.

5. If X is a binomial random variable then its mean is E[X]=?x=npE[X]=?x=np and its standard deviation is ?x=?np(1?p)?x=np(1-p) .

For the next three questions of the following examples, decide whether X is a binomial random variable using ONLY the information given. State why or why not.

Question 1: The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city, and asked whether he or she opposes the death penalty; X is the number who say Yes.

No, more than two outcomes.

Yes, meets all requirements of a binomial random variable

No, probability is not the same for each person.

No, trials are not independent.

Question 2: Suppose a jury of 12 people is chosen from the above pool, and this jury hears a case and discusses the verdict; X is the number who think the defendant is guilty.

Yes, meets all requirements of a binomial random variable.

No, there is not a fixed number of trials.

No, the trials are not independent.

No, there are more than two possible outcome

Question 4: Using the information from the previous question, find the expected number of people cured, i.e., E(X)E(X)(answer in decimal form round to nearest tenth if necessary).

E(X)=E(X)= people

Question 5: Now find the standard deviation of the number of people cured X (answer in decimal form round to nearest tenth if necessary).

SD(X)=SD(X)= people

Question 6: If 31 of the 40 people were cured, would this be unusual?

No

Yes

Also recall that the standard deviation of a Poisson is the square root of the mean: E(X)=?xE(X)=?x (also commonly written as ?? ) and SD(X)=?x=??SD(X)=?x=? .

Suppose a pet clinic gets an average of 9 cats per day to be spayed, and they only have the resources (material supplies and volunteer time) to spay a maximum of 14 cats on any given day. Can we find the probability that more cats will show up on a day than they can spay? We could work with the theoretical distribution, but instead, lets estimate it using relative frequencies in JMP. But FIRST let’s answer some theoretical questions:

Question 1: What are the theoretical expected value for the number of cats showing up at the clinic on a given day (don’t over think this)?

E(X)=E(X)= cats/day

Question 2: What is the theoretical standard deviation for the number of cats showing up at the clinic on a given day? Round to two decimal places.

SD(X)=SD(X)= cats/day

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