Problem 10RE

Phone Calls In the month preceding the creation of this exercise, the author made 18 phone calls in 30 days. No calls were made on 19 days, 1 call was made on 8 days, and 2 calls were made on 5 days.

a. Find the mean number of calls per day.

b. Use the Poisson distribution to find the probability of no calls in a day.

c. Based on the probability in part (b), how many of the 30 days are expected to have no calls?

d. There were actually 18 days with no calls. How does this actual result compare to the expected value from part (c)?

Answer :

Step 1 of 1

a)

Since author made 18 phone calls in 30 days,the mean number of call per day is

=

=

= 0.6

b)

We use the Poisson distribution to find the probability of no calls in a day.

= 0.6

Then the probability of the poisson distribution is

P(x) =

Then,

P(0) =

P(0) = 0.549

Hence the Poisson distribution to find the probability of no calls in a day =0.549

c)

Let the 30 days are expected to have no calls.

The 30 days are expected to have no calls 19.

= 30 P(0)

E(x) = 30 (0.549)

E(x) == 16.5

Therefore the 30 days are expected to have no calls = 16.5 days

d)

There were actually 18 days with no calls.

The expected number of days is 16.5, and that is reasonably close to the actual number of days which is 18.