00:01
For this problem, a particular telephone number is used to receive both voice calls and fax messages.
00:09
Now we assume that 20 % of the incoming calls involve a fax message, and we take a sample of 20 incoming calls.
00:16
So this follows a binomial distribution with n is equal to 20.
00:20
P is 20 % 0 .2, and then q represents 1 minus p, so that is 0 .8.
00:27
The probability function for a binomial distribution is given below.
00:30
So for the first question we are to determine the probability that at most four of the calls involve a fax message.
00:40
So the probability that x is less than or equal to 4.
00:46
So the range of values of x that 4 within this range is the probability that x is 0 plus the probability that x is 1, all the way to the probability that x is 4.
01:01
So we're going to use the summation sign to simplify this.
01:05
So you have a summation sign from x is equal to 0 to 4.
01:12
Then we stick the function.
01:15
We have 11 combination x times p, which is 0 .2, waste to the power x times 0 .8, raised to the power 11 minus x.
01:39
So this is going to substitute the values of x from 0 to 4, compute the individual probabilities, and sum them together and that is equal to 0 .630...