According to a 2017 survey conducted by the technology...

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

Key Concepts

Expected Value in Poisson Distribution

The expected value or mean of a Poisson distribution is equal to the rate parameter ? for the given time interval. This property is used to predict the average number of events expected over different time periods by appropriately scaling ?.

Time Scaling in Poisson Processes

In Poisson processes, the average rate parameter ? scales linearly with time. If the average rate is given for a certain time period, then for a different time period the new rate is computed by multiplying the original rate by the fraction of the time period relative to the one given.

Probability Mass Function (PMF)

The PMF of the Poisson distribution provides the probability of observing exactly k events. It is given by the formula P(X = k) = (?^k * e^(-?)) / k!, where ? is the average number of events, k is a non-negative integer, and e is the base of the natural logarithm.

Poisson Distribution

The Poisson distribution is a discrete probability distribution used to model the number of events occurring within a fixed interval of time or space, under the hypothesis that these events occur with a constant mean rate and independently of the time since the last event.

Complement Rule

The complement rule in probability is used to simplify calculations by determining the probability of an event by subtracting the probability of its complement from one. For example, to compute the probability of receiving at least three events, one subtracts the probability of receiving two or fewer events from one.

Transcript

Please give Ace some feedback