Problem 2. The number of customer service inquiries a help-desk receives in a given hour during normal business hours (Monday through Friday, 08:00 to 17:00) is a random variable that can be modelled by the Poisson distribution, with a rate of 8.4 calls per hour.

a)What does this rate represent?

Always,

Typically, on average,

At least once,

The number of calls that happen in an hour is ____?

b) How many calls would you expect in half an hour?

c)What is the probability that the help desk will receive

(i) six calls in a given hour?

(ii) between five and ten calls (inclusive) in a given hour?equation editor

(iii) three calls in a 30 minutes?equation editor

d)During the first hour (08:00 to 09:00), the help desk received an unexpected 16 calls, what is the probability that something this unexpected would happen.

e) Does this suggest that the number of calls the help-desk receives is higher than 8.4?

Yes, this seems unusually rare, unless the rate is actually higher than reported

Yes, this seems unusually rare, unless the rate is actually lower than reported

No, although this is unexpected it's not that strange, it is still very possible

Yes, it is impossible for this to happen