Final answer:
The random variable X represents the number of books taken out by a patron. We can calculate probabilities and averages using the given information.
Step-by-step explanation:
The random variable X for this example represents the number of books taken out by a patron.
P(x > 2) is the probability that a patron will take out more than 2 books.
The probability that a patron will check out at least one book is 1 minus the probability of taking out no books.
The probability that a patron will take out no more than three books is the sum of the probabilities of taking out 0, 1, 2, or 3 books.
If the table listed P(x) as 0.15, you would know there was a mistake because the sum of all probabilities should be equal to 1.
The average number of books taken out by a patron can be found by multiplying each number of books by its probability and summing the products.