Question

Determine which of the given procedures describe a binomial distribution.

a. Record the number of songs downloaded in a month for a group of 30 randomly selected college students.

b. Observing that ten out of the next twenty customers at a grocery store checkout yse a credit card given that the probability of using a credit card is 0.58.

c. Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.

d. Surveying every 5th person going into a department store to determine age groups of customers.

Answer 1

Here, we have to tell which of the given four procedures describes a Binomial Distribution.

a. Record the number of songs downloaded in a month for a group of 30 randomly selected college students.

b. Observing that ten out of the next twenty customers at a grocery store checkout yse a credit card given that the probability of using a credit card is 0.58.

c. Surveying customers entering a sporting equipment store until a customer responds that he or she was shopping for a bicycle.

d. Surveying every 5th person going into a department store to determine age groups of customers.

ANSWER:- Here notice that,

1.In a. X is the number of songs downloaded and can take any values from 0,1,2,....

2. In c. X is a Geometric Random Variable (number of trials before the first success)

3. In d. It is a simple random sampling experiment.

4. In b. We have X: next 20 customers at the grocery store checkout.

And we are interested in the event

E: next 10 out of 20 people at the grocery store checkout say yes to credit card.

We are also given the probability of using a credit card is 0.58

Hence, here X ~ Binomial (n=20, p=0.58)

Hence, option B) describes a Binomial Process.

This answers your question.

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