HW 4 Due Feb 20
1) Blast shields are going to be placed 10 feet from an explosion. The amount of radiation the shield will
absorb is N(7, 1.22) J/kg.
a) What is the probability that a randomly placed shield will absorb more than 9 J/kg?
0.04746
b) What is the probability that an average of 6 shields will absorb more than 9 J/Kg? 0
2) The amount of stress an IG-88 bolt made by MetalCraft can take before shearing is randomly
distributed with a mean of 1500 pounds and a standard deviation of 30 pounds. A competitor,
StealWorks has manufactured a bolt that they claim is just as good for a lot cheaper. You purchase 50 of
StealWorks new bolts, and test each bolt. The average shear strength was only 1490 pounds. If this had
been a sample of MetalCraft bolts (so that you could use the µ=1500 and σ=30) how often would a
batch of 50 bolts have an average of 1490 or less? 0.0091
3) If the Engineering Building catches fire the amount of heat the structural support beams will be
subjected to is N(1500, 2002) degrees. A random sample of 12 beams is going to be used to experiment
on the beams by putting them in a simulated fire and measuring the temperature.
a) What is the probability that average temperature for the 12 beams will be more than 1527.7
degrees? 0.3156
b) The actual results (not 1527.7°) were surprising – the model predicted the average would be this
high or higher only 2% of the time. What temperature was the average? 1618.5
4) The stop light at the corner of Grand and 19th street stays red for a random amount of time
distributed something bizarre with mean 180 seconds and variance 361 seconds.
a) I swear that light still hates me. I have timed it every day for the past 31 days, and my average
was 184 seconds. How often does that (or a longer average) happen? 0.1210
b) What two times mark the most likely (middle) 95% of averages for 30 days? (173.31, 186.68)
(as a hint a picture of what this is asking is shown below)
5) Brandon wants to find a cheap computer, but he knows that computer prices are extremely skewed,
since most computers are very expensive. He knows that computer prices have a mean of $1,700 with a
standard deviation of $1000. Brandon finds the average price of 9 random computers. What is the
probability the average price will be more than $2,500? Correct answer: I don’t know. You can’t use the
CLT, because n is less than 30. The distribution wasn’t normal beforehand, so we cannot find any
probabilities with our tools.
6) The average price for an acre of land in Wyoming is N(2500, 7002) in dollars. Jaime surveys 49 plots
of land in the Albany county to make sure that they are priced the same as the rest of Wyoming.
Assuming that the Albany county is actually priced similar to the rest of Wyoming, find the probability
that the first plot of land that Jaime surveyed had a price higher than $3,000.
x-bar ~ N(2500, 7002/49) = N(2500, 1002)
But this is asking about the first plot of land, not the average plot of land. So don’t use this above (you
were given too much information).
Z = (3000-2500)/700 = .7142857
The approximate probability from the z table is .7611
We want the probability of being higher, .2389
7) The amount of time it takes you to complete the homework is supposed to be normally distributed,
with a mean of 4 hours, and a standard deviation of 1.5 hours. Chris wants to prove that the homework
actually takes a lot longer than that. Chris randomly selects 4 assignments, and calculates the average
amount of time it takes to complete an assignment. If the Z-score Chris gets is greater than 4 then we
will agree the homework is too hard. What does the mean of Chris’ study need to be for that to
happen?
Z=(x-mu)/sigma
Sigma = 1.5/sqrt(4) = .75
4 = (x – 4)/.75
x=7
The mean needs to be 7 hours
8) Mallory has discovered that the amount of time it takes for a dollar bill to turnaround is distributed
N(19,81) (in weeks). Sadly she absolutely refuses to tell Patrick, and so Patrick is forced to sample
random dollar bills to try to figure out the mean for himself. Assume Mallory is correct, and that Patrick
plans on sampling 9 people.
a) What is the probability that Patrick’s sample average will be more than 20?
The distribution of x-bar is N(19, 81/9) or N(19, 32)
So to find the probability of being greater than 20, Find the z score:
Z
20  19 1
  .333
3
3
Look that up on the Z-table: 0.6293
p-value= 1-.6293= 0.3707
b) Patrick took his sample and his average was 22.57. Now what is the probability that his sample
average is more than 20?
BUT if Patrick got 22.57 then the probability of being greater than 20 is 100%=1
c) What is the probability that the true average turnaround time is greater than 20?
BUT the true mean is still 19, so the probability that it’s above 20 is 0%=0
9) According to The Vancouver Sun (December 18, 2010) McDonald’s chicken fajita is labeled as having 5
grams of fat on average with a standard deviation of 1.1 grams. They did a sample of 3 fajitas, and
found the average to be 8.68 grams of fat. If we assume the label is correct, and we assume fat is
normally distributed, what is the probability of an average of 8.68 grams or greater?
It says to assume it is normally distributed.
z
8.68  5
 5.7
1.1
3
Since we want the area to the right of 5.7 standard deviations, we are off the chart, and the
probability of being above that is 0.
10) Jennifer needs to estimate the average age of vets in Denver. The standard deviation of ages is 16
years. She wants the standard error of her mean to be 2.1 years. How many vets is she going to need
to sample to get at least that kind of accuracy?
  16

x 
 x  2.1
2.1 
n
 16 
n 
 2.1 
n  58.04
16
n
2
You have to round up, so she needs 59 veterinarians