Statistics 4220 Test 1
Version 1
NAME: _________________________________________
Do not turn the page until the test begins.
You have 50 minutes
There will be partial credit, so write legibly. Don’t leave any questions blank…
unless you don’t want ANY credit on a problem.
If you do not have a calculator tell me at the beginning of the test.
I have put the amount of time I believe each question should take to help me
make the exam, and left it on to help you pace yourself.
It may be no surprise that the points for each question are relative to the time it
takes to do the problem.
There will only be partial credit if I can understand your work.
Answers which do not show work (as in the equation used to get the answer)
will not receive full points. I will assume you guessed lucky (or used a nice
calculator) without understanding the procedure involved.
Please silence your cell phone.
No one wants to hear “My Heart Will Go On” during a test.
(1 – 10 minutes)
The temperature of an oil drill that is working properly is N(100, 22)° F. The inspector measures the
temperature, and if the temperature is above 106° F he will shut down the machine and halt the drilling
for routine maintenance and inspection. Of course that’s a big deal, so to be sure he checks the
temperature twice (an hour apart so the measurements are independent) and only shuts down the
machine if both measurements are above 106° F. Assuming a drill is working properly, what is the
probability that the temperature will be above 106° F on the first measurement AND above 106° F on
the second measurement?
(2 – 8 minutes)
The Uniform distribution is useful when you are waiting for something that happens periodically, but
you don’t know when it last occurred (like waiting at the bus stop for the next bus). The uniform
distribution is constant (the density curve looks like a flat line). Assume the bus comes every 24
minutes, then
f ( x) 
1
for 0<x<24
24
What is the variance of this Uniform Distribution, σ2?
(3 – 5 minutes)
The height of randomly selected hammers is distributed N(24, 25) centimeters. I plan on sampling 10
hammers. Find the value of the average such that the probability of getting an average greater than
that is 90%.
(4 – 7 minutes)
When a brick shears the number of pieces it breaks into has the following distribution:
Pieces
Probability
2
0.25
3
0.28
4
0.11
5
0.09
6
0.08
What is the standard deviation of the number of pieces you expect from the sheared brick?
(5 – 3 minutes)
5) Given the boxplot shown what is a reasonable guess for the mean?
A) 0
B) 0.25
C) 0.5
D) 1
E) 3
7
0.19
(6 – 4 minutes)
The salary of a civil engineer in Wyoming is N(70, 122) thousand dollars.
The salary of a civil engineer in Texas is N(50, 82) thousand dollars.
Horace is a civil engineer in Wyoming who makes 84.76 thousand dollars. He’s going to move to Texas,
and although he knows this will be a pay cut he is hoping to make relatively the same level of salary.
What salary should Horace be expecting?
(7 – 12 minutes)
The following data was randomly taken from a normal distribution. Based on the data estimate the
parameters, and then find the probability of getting numbers greater than 10 (assuming the parameters
are correct).
1,
7,
6,
7,
9
(8 – 1 minute) (you can’t get this wrong unless you leave it blank)
If a statistician got into a smack-down fight with a WWF wrestler, who would win?