Question

For one statistics course, among the students who purchase textbook, 60% choose physical textbook, 40% choose electronic textbook. Assume three students who made the purchase are randomly selected. Let random variable X be the number of students chosen physical textbook.
1.(6) find the probability distribution of X.
2.(4) Find the mean of and the standard deviation of X

Answer 1

1.

We are given that among the students who purchase textbook for a statistics course, 60% choose electronic textbook. It means that if a student who made a purchase is randomly selected then the probability that he/she chose physical textbook is equal to 60% = 0.6.

Now, we are given that X is the number of students who chose physical textbook out of the three randomly selected students who made a purchase.

Since, there is a fixed number of students who made a purchase (equal to 3), each student who made a purchase has two outcomes (purchasing a physical textbook and not purchasing a physical textbook) and each student who made a purchase chooses a physical textbook with probability 0.6 independent of other students. Thus, we can conclude that the distribution of X is given by:

X ~ Binomial(n = 3, p = 0.6) [ANSWER]

2.

The mean of X is given by:
E(X) = np = 3*0.6 = 1.8 [ANSWER]

The standard deviation of X is given by:

For any queries, feel free to comment and ask.

If the solution was helpful to you, don't forget to upvote it by clicking on the 'thumbs up' button.