Math 135 Extra Credit
For each question that is COMPLETELY correct, the listed number of points will be added to either test 1
or test 2. All points must be added to either one test or the other. Under no circumstances will I assign a
grade higher than 105 on any particular test. While you may work with classmates on this assignment, no
LAC help/outside tutor help is to be given. You may also ask questions of your instructor.
Neatness counts! Work should be organized, written on loose leaf paper with all StatCrunch output
attached (all pages should be stapled together). Work that is submitted that does not meet this criteria will
not be graded.
Due: Friday, November 15 (NO EXCEPTIONS!!! This is BONUS work!)
Assign points to (circle one) TEST 1
TEST 2
1. (2 points) Rollflex and Morgan Trust are two stocks traded on the New York
Stock Exchange. For the past seven weeks you recorded the Friday closing prices
for each as follows:
Rollflex 51 48 49 53 49 49 50
Morgan Trust 53 51 46 50 50 58 54
a. Compute the mean and median for each (by hand)
b. Compute the 5 # summary for each (by hand)
c. Compute the standard deviation for each (using StatCrunch)
d. Construct side by side box plots to compare the two stocks using StatCrunch.
e. Based on your statistics and graph, can you conclude that one stock generally
gives a higher return than the other? Which stock would be considered more
stable?
2. (2 points) A random sample of 25 orders at a fast-food restaurant was selected and
the dollar amount for each was recorded (rounded to the nearest dollar). The
results were as follows:
12 33 18 13 15 2 23 17 9 11 5 7 12 16 25 29
4
23 7
3 27 14 14 9 6
a. Construct an appropriate graph to determine the shape for the dollar amount spent.
b. Describe the shape and give appropriate measures for center and spread.
c. Can you assume that your data are roughly Normal? Construct an appropriate
graph (using StatCrunch) to check for normality. Defend your answer.
d. If you were to assume that the population is normal, what significance test would
you use to test to see if the true average amount spent for this restaurant is greater
than $15? Explain.
3. (1 point) An SRS of 50 patients is selected from a local blood bank. The
distribution of blood types were found to be the following:
O
A
AB
B
Blood Type
34
12
1
3
Count
a. What is the variable of interest here? Identify the variable as categorical or
quantitative.
b. Construct an appropriate graph to display this variable.
c. Summarize your results (describe the graph).
4. (2 points)* An efficiency expert developed a test measuring job satisfaction of
civil service clerks. An SRS of 10 clerks was selected and the following
information was obtained:
Job
92 32
56
20
72
16
56
76
80
48
satisfaction
Days absent
8
14
10
14
6
17
8
12
7
15
from work
(in one year)
a. What type of relationship is being investigated here? (i.e. QQ, CQ, CC).
b. Treating job satisfaction as your explanatory variable, construct an appropriate
graph to determine whether a relationship appears to exist.
c. Describe the graph in terms of form, direction and strength.
d. Compute the correlation. Compute the least squares regression line and list the
equation.
e. Interpret what the slope represents in the context of the data.
f. Use the regression equation to predict the number of days absent based on a job
satisfaction score of 60.
g. Construct a residual plot. Is there a pattern? What does this indicate?
*Use of StatCrunch is appropriate for the graphs and computations in this problem.
5. (2 points) The Army gives a battery of exams to all new recruits. One exam
measures a person’s ability to work with technical machinery. This exam was
given to a random sample of 360 recruits. The results are shown in the table
below where x is the score on a 10 point scale and F is the frequency of new
recruits with this score.
X
1
2
3
4
5
6
7
8
9
10
F
28
42
79
83
51
36
18
12
7
4
Probability,
P(X)
a. Find the probability distribution for random variable X.
b. Is X discrete or continuous? Explain.
c. Construct a probability histogram for X. Describe the histogram’s shape.
d. Find P(X > 3). Find P(X ≥ 3).
e. The kitchen battalion can use people with a score of three or less. Find the
probability that a new recruit is not overqualified for kitchen duty.
6. (1 point) For each of the following probabilities, shade the area under the standard
normal curve corresponding to the probability. Then find the requested
probability.
a. P(0 < Z < 1.71)
b. P(Z < 0.43)
c. P(Z > 0.43)
d. P(-3.19 < Z < 2.14)
7. (1 point) The snow pack on the summit of Wolf Creek Pass, Colorado on March 1
has been measured for many years by the National Weather Bureau. The depth of
the snow pack in inches is roughly normally distributed with a mean of 78.1
inches and a standard deviation of 10.4 inches. For a given year, find the
probability that the snow pack will be
a. less than 60 inches
b. more than 85 inches
c. between 60 and 85 inches
8.
a.
b.
c.
(2 points) Find the z value such that
10% of the area of the standard normal curve lies to the right of z.
80% of the area of the standard normal curve lies between –z and z.
98% of the area of the standard normal curve lies between –z and z.
(Must show graphs for this problem)
9. (1 point) The life of the Corn Delight popcorn maker is normally distributed with
mean 20 months and standard deviation 2 months. The manufacturer will replace
a Corn Delight popper if it breaks during the guarantee period. How long should
the guarantee period be if the manufacturer does not want to replace more than
3% of the poppers? (round to the nearest month)
10. (1 point) The life of one species of poplar tree is normally distributed with mean
20 years and standard deviation 2.3 years.
a. If one tree is selected at random, what is the probability it will live 21 years or
more?
b. If nine trees are selected at random, what is the probability the sample mean life
of the trees will be 21 years or more? Even though the central limit theorem does
not apply here, why can we assume that the sample mean will follow a normal
distribution?
11. (1 point) The twister roller coaster is one of the top roller coasters in the nation.
There is always a long line of thrill seekers waiting to take a ride. A random
sample of 60 riders waited in line for a sample mean time of 40 minutes with a
sample standard deviation of 12 minutes. Compute a 90% confidence interval for
the true population mean wait time for the Twister coaster. Explain what this
confidence interval represents.
12. (2 points) The Magic Dragon cigarette company claims that their cigarettes
contain an average of only 10 mg of tar. A random sample of 100 Magic Dragon
cigarettes shows that the average tar content per cigarette to be 11.5 mg with a
standard deviation of 4.5 mg. Is this enough evidence to indicate that the true
average tar content of Magic Dragon cigarettes exceeds 10 mg? Conduct the
appropriate significance test. Use α=0.05. List the assumptions, hypotheses, test
statistic, p-value and conclusion.