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Text: Emails Received. According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is five. a. What is the probability of receiving no emails during an hour? b. What is the probability of receiving at least three emails during an hour? c. What is the expected number of emails received during 15 minutes? d. What is the probability that no emails are received during 15 minutes?

          Text: Emails Received. According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is five.

a. What is the probability of receiving no emails during an hour?
b. What is the probability of receiving at least three emails during an hour?
c. What is the expected number of emails received during 15 minutes?
d. What is the probability that no emails are received during 15 minutes?

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Added by Nichole L.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Steven Clarke

08/01/2023

Step 1

The probability of receiving no emails during an hour can be calculated using the Poisson probability formula: P(X = k) = (e^(-λ) * λ^k) / k! where λ is the average number of emails received per hour (5 in this case), k is the number of emails we want to find Show more…

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Text: Emails Received. According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is five. a. What is the probability of receiving no emails during an hour? b. What is the probability of receiving at least three emails during an hour? c. What is the expected number of emails received during 15 minutes? d. What is the probability that no emails are received during 15 minutes?

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Transcript

00:01 Okay, we are told that the number of emails received per hour follows a poisson distribution.

00:06 So you can say then x corresponds to a poisson distribution where the parameter is 5.

00:13 The mean value is 5 per hour.

00:16 I want to work out in one hour the chance that there are zero emails and for that use a ti -84 plus calculator for one similar and what you want is the function poisson pdf, poisson pdf, which you will find by pressing 2nd followed by vars v -a -r -s on the right by the arrow keys.

00:43 That gives the menu for distributions.

00:46 You can't see it yet, but go down with the arrow key past number 9 at the bottom.

00:51 Keep going down till you reach item d, poisson pdf.

00:55 Press enter.

00:56 The input is the mean which is 5 per hour and the x value is 0.

01:05 So just type in poisson pdf 5 0 paste enter and we get 0 .006737 and so on.

01:21 What they want here is no mention of accuracy.

01:27 So we'll say then 0 .00674 correct to 3sf.

01:35 That's the first one.

01:36 Okay, next we have the chance of getting 3 or more.

01:42 So at least 3, which means of course 3, 4, 5, 6, 7, 8, 9 and so on.

01:48 And for this you have to work backwards and do 1 minus what you don't want to occur which is x to be 2 or less.

01:57 Now that i work out again with the ti -84 plus.

02:02 This time the function is poisson cdf.

02:06 Cdf, c stands here for cumulative.

02:09 That will work out for you...

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