Download Set 6 - insead

INSEAD MBA
Uncertainty, Data & Judgement
Exercises
Set 6
(Session 6)
6.1. The CMS department at INSEAD is interested in the mean µ for the consultants’starting
salaries in the US in 1998. The population standard deviation σ is assumed to be
$10,000. A random sample of size n from the relevant population of consultants is
being considered. What is the probability that the sample mean ( X ) will be within
µ ± $5,000 if (a) n = 36, (b) n = 100? Do you need to make any assumptions for your
answers?
6.2. A newly produced BMW car boasts 45 miles per gallon on the highway. Assume that
the distribution of the miles per gallon is a normal distribution with a mean of 40 and a
standard deviation of 5. The Environmental Protection Agency randomly draws 100 of
the new BMWs to test-drive.
(a) What is the probability that a certain car can achieve 45 miles per gallon?
(b) What is the probability that the sample mean of the 100 cars exceeds 45 miles per
gallon?
6.3. A supplier of milk bottles claims that the amount of milk in a 16-ounce bottle follows a
Gamma distribution (a distribution which we haven’t studied in class) with a mean of 16
and a standard deviation of 1. A consumer protection agency buys 30 bottles of milk
and weighs them. What is the probability that the average weight of these 30 bottles of
milk will fall between 15.9 and 16.1 ounces? Do you need to make any assumptions?
6.4. In Exercise 6.1 above, suppose that the CMS department takes a random sample of 100
consultants who started their careers in the US in 1998 and finds the sample mean of the
starting salaries to be $120,000. Construct a 95% and a 99% confidence interval for the
true mean of the 1998 starting salaries for the entire population of consultants in the US.
(Assume the population standard deviation to be $10,000, as mentioned in Exercise 6.1.)