Question

Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.) (a)Compute the probability of receiving three calls in a 5-minute interval of time. (b)Compute the probability of receiving exactly 10 calls in 15 minutes. (c)Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? (d)If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

          Phone calls arrive at the rate of 48 per hour at the
reservation desk for Regional Airways. (Round your answers to four
decimal places.)
(a)Compute the probability of receiving three calls in
a 5-minute interval of time.
(b)Compute the probability of receiving exactly 10 calls in 15
minutes.
(c)Suppose no calls are currently on hold. If the agent takes 5
minutes to complete the current call, how many callers do you
expect to be waiting by that time? What is the probability
that none will be waiting?
(d)If no calls are currently being processed, what is the
probability that the agent can take 3 minutes for
personal time without being interrupted by a call?

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Added by Shawn S.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Supreeta N

03/24/2023

Step 1

Since there are 48 calls per hour, we can divide this by 60 minutes to find the average number of calls per minute: 48 calls/hour * (1 hour/60 minutes) = 0.8 calls/minute Now, we can use the Poisson distribution to compute the probabilities. The Poisson Show more…

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Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. (Round your answers to four decimal places.) (a)Compute the probability of receiving three calls in a 5-minute interval of time. (b)Compute the probability of receiving exactly 10 calls in 15 minutes. (c)Suppose no calls are currently on hold. If the agent takes 5 minutes to complete the current call, how many callers do you expect to be waiting by that time? What is the probability that none will be waiting? (d)If no calls are currently being processed, what is the probability that the agent can take 3 minutes for personal time without being interrupted by a call?

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Transcript

00:02 Hello students, according to the given question we have to find the probability values.

00:07 So here given that phone call, phone call arrive rate is given as 48 per hour.

00:21 So in the a bit here x denote number of calls arrive in five minutes.

00:32 So then x follows poison distribution of lambda.

00:39 Here lambda is 48 into 5 is divided by 60 seconds.

00:45 So that is equal to 4.

00:48 So then the required probability is x is equal to 3 calls.

00:53 So that is equal to e power minus lambda, lambda power x by x factorial by the poison distribution.

01:01 So by substituting e power minus 4, 4 power 3 by 3 factorial, which is equal to 0 .1954.

01:13 Now in the b bit here x denote number of calls arrive in 15 minutes.

01:25 So that means here lambda will be equal to 48 into 15 by 60.

01:33 That is equal to 12.

01:35 So x follows poison of lambda is equal to 12.

01:40 So the required probability is x is equal to exactly 10 calls, that is equal to e power minus 12.

01:48 12 power 10 is divided by 10 factorial, which is equal to 0 .1048.

01:58 Now in the c bit here x denote number of calls arrive in 5 minutes.

02:11 So then lambda will be 48 into 5 by 60.

02:16 That is equal to 4...

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