A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 8 of the calls involve a fax message

99.1% probability that at most 8 of the calls involve a fax message

Step-by-step explanation:

For each call, there are only two possible outcomes. Either it is a fax message, or it is not. The probability of a call being a fax message is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls

This means that

(a) What is the probability that at most 8 of the calls involve a fax message

99.1% probability that at most 8 of the calls involve a fax message

use this formula:

p(a\b) = p(a and b)/p(b).

take it from here.