2. The marketing manager of a company has noted that she usually receives 10 complaint calls from customers during aweek (assume a week has 7 days), and that the calls are independent, and assume a Poisson distribution.

(a) Find the probability she receives exactly 5 complaint calls in a week.

(b) Find the probability she receives at least 2 complaint calls in one day.

(c) Find the expected number of complaint calls in a month (assume 30 days in one month).

3. An inspector for air pollution decides to inspect 8 of a company's 16 trucks. 5 of those trucks have pollutants above the accepted level. Assume the trucks the inspector looked at were selected randomly.

(a) What is the probability that he finds exactly 3 trucks with pollutants above the accepted level?

(b) What is the probability that he finds at least 3 of the trucks with pollutants above the accepted level?

(c) What is the expected number of trucks with pollutants above the accepted level he will find?

4. Suppose the length of time students take in writing a standard entrance examination is normally distributed with mean 60 minutes, std. deviation 8 minutes.

(a) Find the probability that a randomly selected student takes between 60 and 70 minutes to write the exam.

(b) Find the probability that a randomly selected student takes at most 80 minutes to write the exam.

(c) If a randomly selected student has taken over 40 minutes, find the probability they will take at most 80 minutes to write the exam.

(d) Find the 50th percentile for the time it takes for students to write the exam.

5. Mensa is an organization whose members possess IQ's in the top 2%. It is reasonable to assume IQ is normally distributed with mean 100 and standard deviation of 16.

(a) Find the IQ needed to be a member of Mensa.

(b) All students at a particular university have an IQ over 120. If a random student from this university is selected, find the probability their IQ is above that needed to be accepted to Mensa.

(c) Find the probability that a random persons IQ is above 120.