Statistics 4220 Test 1
Version A
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.
So a 4 minute question is worth 8 points
The minutes add up to 50.
For this test you may use a page of notes, a calculator, and z-tables
If you need any of these let’s find a solution at the beginning
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 the “Yo Gabba Gabba” song in the middle of the test
1 (1 minute)
You are told that the IQ of college students is normally distributed with a mean of about 112.
Therefore, you can conclude that the median IQ of college students is ______________.
2 (1 minute)
The distribution of annual incomes for US household is right skewed. If the Census bureau reports a
median annual income of $47,500, this implies that the mean annual income is:
About the same
Larger
Smaller
Cannot determine
The distribution for the load on a bridge (in Newtons) at a random time has a distribution with pdf

f ( x)  4 x  x 3

for 0 < x < 1
3 (3 minutes)
What is the expected load on the bridge at any random time?
4 (5 minutes)
What is the standard deviation of the load on the bridge?
5 (2 minutes)
A survey asked board members which building plan they preferred for a hotel lobby,
Plan 1 (with a waterfall), Plan 2 (with large screen TV’s), or Plan 3 (Jungle themed).
The probability that a board member will like each plan is shown in the table below
Plan
Probability
1
0.30
2
0.60
3
0.10
The boss wants to know the expected value. What would you tell him?
6 (4 minutes)
The amount of pressure in a randomly selected scuba tank has an average of 180 PSI with a standard
deviation of 13 PSI. McGyver just found 4 random scuba tanks. If the average pressure is above 212,
then hitting the valves with a beam will make the tanks shoot a doorway through a brick wall. What is
the probability this will make a door?
7 (5 minutes)
The following 5 data points came from a normal distribution. Based on the data, engineers estimated
the distribution was N(24, 372). Show how they got those numbers.
1
3
8
19
89
8 (4 minutes)
The MSS-1.2 AC is an anti-tank missile cluster used in Brazil. The cluster flies 8 simultaneous missiles 50
yards off the ground until it reaches its target. The actual height off the ground per missile in the cluster
is N(50, 252). If the average height is actually only 30 yards off the ground it is considered dangerous by
the UN. What percentage of the time will a cluster be considered dangerous?
9 (6 minutes)
The American Creative Machinery Engineers manufactures jet packs that are supposed to last 12
minutes. Unfortunately some of the jet packs are defective. The company wants to offer a refund to
customers who have a jet pack that quits too early. They only want to refund 4% of their customers.
Assuming the distribution is normal with a standard deviation of 6.29 minutes, they should refund jet
packs that last shorter than what length of time?
10 (3 minutes)
A jet is being scrambled to attack an insurgent camp. Anti-aircraft missiles are randomly fired at the jet
from enemy positions along the route. The commanding officer has decided that if 8 missiles or more
are fired at the jet before it can attack then he will scrub the mission. The jet needs 15 minutes to reach
the insurgent camp. The commanding officer wants to know the probability that the jet will make it to
the camp before the mission needs to be scrubbed. What distribution would be a natural choice for him
to use?
11 (5 minutes)
The number of JSON requests per minute to the server of the www.BoringLongOutdatedGossip.com
website has the pdf f(x) shown below (they never have more than 5 requests per minute).
X (pings)
f(x)
F(x)
0
0.40
0.40
1
0.30
2
0.20
3
0.05
4
0.03
What is the probability of getting 1 ping or fewer?
What is the probability of getting 2 pings or fewer?
Now fill in the rest of the CDF, F(x), which is the third row shown in the table.
5
0.02
12 (3 minutes)
Match the histogram shown below to the appropriate boxplot
13 (3 minutes)
When children jump on a bed the amount of force on the bed per child is N(445, 169) Newtons. As long
each child is at a different corner and the average force is below 517 Newtons then the bed should be
fine. What is the probability that my bed will be fine if my four kids jump on each corner of my bed
while I write test questions?
14 (4 minutes)
The distribution of radiowaves is normal, which includes satellite communication on the high end and
maritime channels on the low end. A 1960’s ham radio can pick up signals in the range shown by the
shaded region on the graph. Calculate the percentage of radio signals that the 1960’s ham radio can
detect (show how you are calculating the area, don’t just guess)
15 (1 minute)
What should a statistician do for the world’s greatest wife for Valentines? (budget: $10, rated PG)