Midterm Exam 1
QBA 201 – Summer 2013
Instructor: Michael Malcolm
Instructions: You can use any written materials you would like in completing this
exam, and a calculator.
Statement of academic honesty:
This exam entirely reflects my own work. I have not received assistance from
anyone or given assistance to anyone in completing this exam
Signature: _________________________________
Name:
_____________________________________
For each question below, construct a dataset with the required properties.
a. Construct a dataset that contains 4 observations such that the mean is 6 and the standard deviation is 0.
{𝑥1, 𝑥2, 𝑥3, 𝑥4} = {____, ____, ____, ____}
b. Construct a dataset that contains 2 observations such that the geometric mean and the arithmetic mean are both equal to 4.
{𝑥1, 𝑥2} = {____, ____}
c. Construct a dataset that contains 2 observations such that the geometric mean is 4 but the arithmetic mean is 5.
{𝑥1, 𝑥2} = {____, ____}
d. Construct a paired dataset that contains 3 observations such that the correlation is +1.
60% of mechanics in a town are crooks, while 40% are honest. If you take your car to an honest mechanic, he will fix it properly 90% of the time. On the other hand, if you take your car to a crook, he will only fix it properly 50% of the time.
Americans spend an average of 11 hours each week on the Internet, with a standard deviation of 6 hours.
a. Without any assumptions about the distribution of the data, give three intervals and predict the approximate percentage of the data that will fall in these intervals.
b. If you assume that the distribution of the data is bell shaped, give three intervals and predict the approximate percentage of the data that will fall in these intervals.
Two doctors are on staff at a hospital. Dr. Ahmad is absent 20% of the time. Dr. Bedriya is absent 10% of the time.
a. Suppose that their absences are independent events.
i. What is the probability that both doctors will be absent?
ii. What is the probability that at least one doctor will be absent?
iii. What is the probability that Dr. Ahmad will be absent given that Dr. Bedriya is absent?
b. Suppose instead that their absences are mutually exclusive events.
i. What is the probability that both doctors will be absent?
ii. What is the probability that at least one doctor will be absent?
You have a dataset that consists of 𝑛 observations of some variable, where 𝑛 > 100. The first 𝑛 − 1 observations in this dataset are all equal to 3. The 𝑛’th observation (the last one in the dataset) is equal to 7.
Calculate each of the following summary statistics. Note that some of the answers to the questions below are numbers and some of them are formulas that are functions of 𝑛.
Arithmetic mean
Geometric mean
Harmonic mean
Median
60th percentile
Q1
Q3
Range
IQR
Socioeconomic data show that 10% of married men will experience a job loss in a given year. 15% of married men will have wives who experience a job loss in a given year. 4% of married men in a given year will experience a job loss and will have wives who experience a job loss.
a. Find the probability that, among married men, at least one of the two spouses will lose their jobs in a given year.
b. Given that a married man lost his job, what is the probability that his wife also lost her job?
c. Given that at least one of the two spouses lost their jobs, find the probability that both
There is a horrible disease spreading. If you get the disease, it will turn you into a shrubbery. There are two different tests for the disease – one tests your blood and the other tests your saliva. The tests are very rarely in error. You see on the news that the probability that a randomly selected person will test positive for the first test is 0.2 and the probability that a randomly selected person will test positive for the second test is also 0.2.
Your friend intends to have both tests done. Knowing that you are an expert in probability, he asks you: “What is the probability that both tests will turn out positive?”
a. What would the correct answer be if the test results were independent?
b. Do you think that the two test results are actually independent? Explain.
Every day you pass by two police officers checking for speeders. The first police officer catches speeders 1% of the time. The second police officer catches speeders 2% of the time. The two officers act independently of each other.
