Question

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. Suppose for a particular office, the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is seven. (Round your answers to four decimal places.) (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?

          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. Suppose for a particular office, the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is seven. (Round your answers to four decimal places.)

(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 Kenneth O.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert T. L.

01/03/2023

Step 1

71828). P(X = 0) = (e^(-7) * 7^0) / 0! Plugging in the values, we get: P(X = 0) = (e^(-7) * 1) / 1 = e^(-7) Now, we can calculate the value: P(X = 0) ≈ 0.0009 So, the probability of receiving no emails during an hour is approximately 0.0009. (b) The Show more…

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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. Suppose for a particular office, the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is seven. (Round your answers to four decimal places.) (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 Hey there, welcome to numerade.

00:04 We are given a person distribution, given the average number of emails received an hour, which is 7.

00:12 So this will be represented as lambda.

00:15 So here, lambda will equal 7.

00:25 All right.

00:26 So knowing this here, we're asked to find a probability of receiving no emails during that hour.

00:33 So we're going to be using the person distribution equation, where we have the probability of x raised to which is the e constant raised to the negative lambda multiplied by lambda raised to the x divided by x factorial a over here we're going to be looking for no emails which is zero emails so the probability of zero equals e raised to negative 7 multiplied by 7 raised to the 0 divided by 0 factorial, simplifying to a probability of around 0 .009.

01:24 Alright, so this is our probability here.

01:30 0 .0009.

01:34 Okay, so for part b, we're asked to find a probability of receiving at least three emails during an hour.

01:42 So the probability where x is greater than or equal to three, which is basically equivalent to one minus the probability where x is less than three.

01:55 So we're going to plug in this probability into our equation above again.

02:00 So this equation.

02:02 Therefore, this will give us a probability for at least three emails of a round.

02:15 So at least three emails...

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