Statistics 4220 Test 1
NAME: _________________________________________
Instructions:
Read these instructions
Do not turn the page until the test begins
You have 50 minutes
This test is printed on both sides, so don’t miss a page.
Each question is worth double the number of minutes. This test is timed for 50 minutes.
For this test you may use a page of notes, a calculator, z-tables
If you need any of these please find a solution before the exam begins
If you have a question during the test please come forward quietly so that you are not
disruptive. If you leave early please do so quietly. Note that I cannot give answers that
are part of the test, only clarify the English being used.
You must show your work. Answers which are correct but do not show any work may
not get full credit. I might assume you either guessed, cheated, or used some fancy
calculator.
Cheating is not tolerated. Any inappropriate activity will be discussed after the final
Hats or hoods must be moved so that your face is not obscured.
Please turn off your cell phone. You cannot have your phone out at all.
No one wants to hear your duck quacking during the test.
1) (6 minutes)
The Elgoog Vision Institute Liason is hiring a team of researchers to find the average amount of
time people spend on the internet per day. Each member of the team randomly selects 100
people to survey. Everyone on the team brings back a different average because the true
distribution has an average of 4.5 hours with a standard deviation of 2.5 hours. What bounds
would mark the middle 98% most likely averages? A picture of what is being asked is shown
below (which should remind you of the similar homework problem).
2) (5 minutes)
The following table shows the distribution for the number of computers owned by college
students. Notice that no college student owns more than four computers.
Computers
0
1
2
3
4
f(x)
0.05 0.42 0.36 0.15 0.02
a) What is the median number of computers owned by a college student?
b) What is the standard deviation for the number of computers owned by a college student?
3) (3 minutes)
The famous hacker Yppilc has created a virus that is designed to infect a computer and then
spread to any nearby computers networked to it within days. Yppilc wants to know how likely it
is that it will infect over a million computers within a month. What distribution should Yppilc
use to help him calculate that probability?
4) (5 minutes)
An artificial heart pump is meant to push 78 gallons of blood per hour, with a standard deviation
of 7 gallons per hour. We want to know the probability that a randomly selected heart pump
will push more than 69.6 gallons of blood per hour. Don’t answer the probability itself. Instead
shade in the probability using the blank normal curve shown below.
5) (3 minutes)
The Tines company makes screws that are 1.2 inches long. The standard deviation for their
screw lathe is 0.022 inches for the length. The quality control engineer is checking whether the
screw lathe is on spec by randomly sampling 25 screws. What is the probability that the average
length of her sample will be less than 1.1912?
6) (5 minutes)
When a new applet is designed for the IPhone the memory size is random, but normally
distributed with a mean of 1.6 GB and a standard deviation of 0.5 GB. What is the probability
that a randomly chosen applet will have between 0.88 and 2.56 GB?
7)
(3 minutes)
The distribution of time for an Apache server to kill an infinite while-loop is distributed as
f(x) = 3/704 * x2- 6/704 * x for 2 < x < 10 in minutes.
What is the probability that on a random while-loop the server will kill it at exactly 8 minutes?
8) (3 minutes)
When a random Hot-Pocket is microwaved for 1.5 minutes the amount of radiation it will
receive is normal with a mean of 40 MsV and standard deviation of 1.8 MsV. If I take a random
sample of 42 Hot-Pockets what is the probability that I would get an average above 40.5 MSV?
9)
(5 minutes)
A sample of 72 randomly selected Cricket Wireless phones finds the average number of bars is
2.72. According to Cricket’s advertising, the average is supposed to be 2.83 bars with a standard
deviation of 0.15 bars. If their advertisement was correct then what would be the probability of
getting an average like we observed in our study or something even lower?
10) (5 minutes)
The average temperature for a Lenovo laptop that has been running continuously for 5 hours is
N(101, 4.84)° F. The secondary fan is designed to kick in only for the hottest 2% of laptops.
What temperature would mark the hottest 2% of these laptops?
11) (6 minutes)
The distribution for the depth of a randomly chosen well in South America is


f ( x)  k x 3  1
for 0 < x < 3 in kilometers
a) Find the value of k that makes the distribution a valid probability distribution.
b) Find the cumulative density function, F(x)
c) What is the probability of a randomly chosen well having a depth less than or equal to 2
kilometers?
12) (1 minute)
If we could magically transport our class anywhere in the world, where do you think would be
the best place for a summer class on statistics?