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Lilyy1k
14.02.2020 •
Mathematics
The probability that your call to a service line is answered in less than 30 seconds is 0.85. Assume that your calls are independent. (a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654). (b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654). (c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.
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Ответ:
a) 0.1720
b) 0.8298
c) 19
Step-by-step explanation:
For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. 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.
In this problem we have that:
(a) If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is
when
.
So
(b) If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).
This is
when ![n = 20](/tpl/images/0511/5192/9ca0b.png)
So
So
(c) If you call 22 times, what is the mean number of calls that are answered in less than 30 seconds? Round your answer to the nearest integer.
The expected value of the binomial distribution is:
In this question, we have![n = 22](/tpl/images/0511/5192/96b02.png)
So
The nearest integer to 18.7 is 19.
Ответ:
A≈50.27in²
Step-by-step explanation: