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 three. (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?

The interval of interest is per hour. This means 60 minutes. Since the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three, it means that

Mean, μ = 3

x is a random variable representing the number of mails received per hour

a) The probability of receiving no emails during an hour is expressed as

P(x = 0)

From the Poisson distribution calculator,

P(x = 0) = 0.0498

b) the probability of receiving at least three emails during an hour is expressed as P(x ≥ 3).

P(x ≥ 3) = 0.577

c) the expected number of emails received during 15 minutes is

3 × 15/60 = 0.75

d) mean = 0.75

From the poisson distribution calculator, P(x = 0) = 0.47