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

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.