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.
1) (5 points)
The distribution for the lifetime of a random capacitor is N(143, 64) in months. A random
sample of 4 capacitors found an average of 150.2 months. The graph below shows the sampling
distribution for average capacitor lifetimes from samples of size 4. Mark on the graph where the
sample average should land on this picture (ticks marks show standard errors).
(Make it clear where your mark is)
2) (3 minutes)
When you drop a cellphone there is a 50% probability no cracks will appear. If it does crack the number
of cracks than can appear is between 1 and 4 cracks, and the distribution is based on the cell phone
company. It have been determined that for Cricket Cell phones the distribution is
Number of cracks:
f(x)
0
0.50
1
4k
2
2k
3
k
4
k/2
Find the value of k that makes the distribution above a true discreet pdf.
3) (5 minutes)
The distribution of the force (in tons) for a randomly selected test dummy car crash follows the pdf
f ( x) 

20
3x 3  x 4
243

for 0 < x < 3
What is the probability that a randomly selected test dummy car crash will have a force of less than 1
ton?
4) (5 minutes)
A random sample of 5 humans studied the mass of each human. It is assumed that the distribution is
normal. The statistician who analyzed the data decided to claim that the distribution for mass of a
random human must be close to N(65, 112). Below are shown the 5 masses from the sample. Using
those values show how the statistician would have found the 65 and 11.
Show how you calculated it (Don’t just give an answer from a fancy calculator, I need to see you know how to do it).
56, 57, 60, 82, 70
5) (5 minutes)
When a drone is instructed to fly straight up for 1000 feet the number of feet that it actually climbs is
random with distribution N(1000, 1.72). If a randomly selected drone is instructed to fly straight up for
1000 feet, what is the probability it will not reach an altitude over 1004 feet?
6) (4 minutes)
When a package of Mentos is put in a Coke bottle the bottle will rocket (straight up if it is put on a
track). The height is distributed normally with a mean of 6 feet and a standard deviation of 1.4 feet.
What height marks the highest 4% for rockets of this type?
7) (3 minutes)
Apple records the color of an Ipad when it is ordered with the following system:
001: Silver
002: Black
003: Red
004: Yellow
They have a table showing the frequency of orders for each color:
Color:
Frequency:
001
0.60
002
0.20
003
0.12
004
0.08
The Apple Executive needs to the know the mean for the colors in the table above.
What would be your answer?
8) (4 minutes)
The time it takes an architectural engineer to graduate is normally distributed with a mean of 4.8 years
and a standard deviation of 0.6 years. If we randomly select an engineer what is the probability it will
take him/her longer than 10 years to graduate?
9) (4 minutes)
A random sample of 25 engineers asked them how many minutes per day they spend on the internet. If
the true distribution for all Engineers has a mean of 200 minutes per day with a standard deviation of 70
minutes per day, what is the probability that the sample average will be more than 215.876?
10) (6 minutes)
The time it takes a DELL laptop battery to charge (from completely dead) is randomly distributed with a
mean of 350 minutes and a standard deviation of 120 minutes. If we randomly sample 100 laptops and
time how long it takes them to charge (from dead) what is the probability that our average would be
between 334 and 376?
11) (5 minutes)
Fred checks the temperatures of the heating units at Smallville high by touching each of the 25 heating
coils by hand. The temperature of a heating coil is N(110, 52)° F. If the temperature is over 122° F then
Fred will get burned. He now only has the last heating coil, the 25th heating coil left to check. What is
the probability that coil will give Fred a burn?
12) (1 minute)
In a zombie apocalypse, what would be the role of a statistician?