For each of the experiments listed below, chose what distribution would be appro

Question

For each of the experiments listed below, chose what distribution would be appropriate to use.

You can use each distribution more than once.

A – Binomial

B – Multinomial

C – Hypergeometric

D - Geometric

E - Negative Binomial

F - Poisson

________ A collection of 37 rare coins contains 6 counterfeits. Three of these coins are randomly selected to be sold to a dealer. We are interested in the number of counterfeits that the dealer receives.

________ It has been seen that 9% of the patients who are given a certain medicine will have undesirable side effects. We are interested in the number of patients who experience side effects from a sample of 18 that are given this medicine.

________ The probability that a student pilot passes the written test for his private pilot’s license is 0.80. We are interested in the probability that a student picked at random passes the test on his third try.

________ A multiple choice test has 25 questions, each with 4 possible answers of which only 1 is correct. We are interested in the number of correct answers if the test is filled out only by guesswork.

________ On average, a person fishing at a particular lake will catch 2 fish per hour. We are interested in the number of fish a randomly selected person will catch in an hour.

________ A hand of five cards is dealt from a standard 52 card deck. We are interested in the number of Aces in the hand.

________ Suppose the probability that a basketball player makes a foul shot is 0.70. We are interested in the number of shots he will have to take in order to make 3 of them.

________ A study has shown that in a certain city 70% of all families own at least 2 TV sets. We are interested in the number of families that own at least 2 TVs from a sample of 20 families.

Explanation / Answer

Solution:-

1) Binomial - A collection of 37 rare coins contains 6 counterfeits. Three of these coins are randomly selected to be sold to a dealer. We are interested in the number of counterfeits that the dealer receives.

2) Binomial - It has been seen that 9% of the patients who are given a certain medicine will have undesirable side effects. We are interested in the number of patients who experience side effects from a sample of 18 that are given this medicine

3) Negative Binomial or geometric - The probability that a student pilot passes the written test for his private pilot’s license is 0.80. We are interested in the probability that a student picked at random passes the test on his third try.

4) Binomial - A multiple choice test has 25 questions, each with 4 possible answers of which only 1 is correct. We are interested in the number of correct answers if the test is filled out only by guesswork.

5) Poisons - On average, a person fishing at a particular lake will catch 2 fish per hour. We are interested in the number of fish a randomly selected person will catch in an hour

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