1. The time that a technician requires to perform preventative maintenance on an air-conditioning unit is
governed by an exponential distribution with a mean of 60 minutes and a standard deviation of 60 minutes.
Your company operates 70 of these units. What is the probability that their average maintenance time
exceeds 50 minutes?
2. Your company produces various mechanical parts for a food processing company. Your inspectors check the
parts you produce and over a long period of time have seen that on average, 3% of all products you produce
are “defective”. Luckily, the food processing company you ship to will allow for a maximum of 5%
defective parts for each package you send them, otherwise they will send the shipment back to you. If their
shipment contains 80 parts, what is the probability they send the box back?
3. Continuing the scenario of number 2. If you wanted to be 99% sure that the food processing company will
accept a shipment, how many parts should you include in the shipment?
4. The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per
mile and standard deviation 0.15 g/mi. A company has 125 cars of this model in its fleet. What is the level L
such that the probability that the sample mean is greater than L is only 0.01?
5. The NCAA requires Division I athletes to score at least 820 on the combined math and verbal parts of the
SAT exam to compete in their first college year. In 2002, the scores of the 1.3 million students taking the
SATs were approximately Normal with mean 1020 and standard deviation 207. What percent of all students
had scores less than 820?
6. The vending machine in Recitation is in need of repair – (for simplicity we’ll say it only takes dollar bills and
everything in the vending machine will cost at most one dollar). For each dollar the vending machine
receives, the vending machine will treat each dollar independently but will only actually give the customer
what they asked for 78% of the time. The other 22% of the time, it will take the dollar without dispensing
anything. The machine received 40 dollars this morning, what is the probability it actually worked (did not
just keep the dollar) between 30 and 35 times (inclusive)?
7. A laboratory weighs filters from a coal mine to measure the amount of dust in the mine atmosphere.
Repeated measurements of the weight of dust on the same filter vary normally with standard deviation of
0.08 mg because the weighing is not perfectly precise. The dust on a particular filter actually weighs 123 mg.
Repeated weighings will then have the Normal distribution with mean 123 mg and standard deviation 0.08
mg. What is the probability that the laboratory reports an average of 30 weighings as 124 mg or higher for
this filter?