Answer:
Step-by-step explanation:
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
