Question

1)During the period of time that a local university takes phone-in registrations, calls come in at the rate of one every two minutes.

a.Clearly state what the random variable in this problem is?

b.What is an appropriate distribution to be used for this problem and why?

c.What is the expected number of calls in one hour?

d.What is the probability of receiving three calls in five minutes?

e.What is the probability of receiving NO calls in a 10-minute period?

f.What is the probability of receiving more than five calls in a 10-minute period?

g.What is the probability of receiving less than seven calls in 15-minutes?

h.What is the probability of receiving at least three but no more than 10 calls in 12 minutes?

Answer 1

A) Clearly state what the random variable in this problem is?

The random variable in this problem is the number of calls.

B) What is an appropriate distribution to be used for this problem and why?

It follows Poisson Distribution because it expresses the probability of a given number of events occurring in a fixed interval of time and/or space, if these events occur with a known average rate and independently of the time since the last event.

Firstly we should find value of = (1/2) * 5 = 2.5

C) What is the expected number of calls in one hour?

E[X] = 2.5 *(60/5) = 30

D) What is the probability of receiving three calls in five minutes?

P[X=3] = e^-2.5 * 2.5^3 /3!

= 0.2138

E) What is the probability of receiving NO calls in a 10-minute period?

P[X=0] = e^-2.5

= 0.0821