MATH 1342 BPS 5th ed.
HW Ch.3 notes
Send corrections / comments to Mary Parker at mparker@austincc.edu
last updated 09/10//09
page 1 of 3
Homework Notes Chapter 3
Chapter 3: [3.1, 3.2, 3.4, 3.5, 3.7, 3.9, 3.10, 3.11, 3.12, 3.13, 3.14, 3.15-3.24], 3.25, 3.27 3.29,
3.31, 3.33, 3.35, 3.36, 3.39, 3.43, 3.45, 3.47, 3.49(M), 3.52(A)
The key to learning the material in Chapter 3 well is to always draw pictures and label them
correctly as part of your solutions for normal calculations even if the answer key doesn’t have
them. (You will be required to do that on the test.) This will also help you retain these skills
until about Chapter 10 when we start using them as a part of solving other problems.
When you look at Table A, be sure to choose the version of the table with the picture at the top
of each page. It’s at the end of the textbook and, in StatsPortal, under “Resources > Tables and
Formulas”. If you’re using the e-book instead of a printed book, please print the table and use
this printed copy.
3.1 Sketches will vary. If you look at Figure 3.7 in Exercise 3.4 at the end of the section on
Describing Density Curves, you can see some examples of sketches that would be OK. See
sketches b and c.
3.2 a. Look at the two conditions on p. 69. Does it fit them?
For the remaining parts, show a shaded picture in addition to computing the answer:
b. 1/3 c. (1.1-0.8)/3 = 0.1
3.4 Graph a. median B and mean C
Graph b. median B and mean B
Graph c. medan B and mean A
3.5 Draw a picture similar to Figure 3.10, but, of course, there are different numbers.
3.7 Draw pictures. Make a picture like Figure 3.10 but with different numbers, and answer the
questions by referring to that picture.
3.10. Draw pictures. a. 0.9978 b. 0.0022 c. 1.0000 – 0.0485 = 0.9515
d. In the copy of the paper textbook I have, the problem is -1.66 < z < 2.85. The solution to that
is 0.9978-0.0485 = 0.9493
d. In the e-book at the time these notes are written, the problem is -1.66 < z < 2.58. The solution
to that is 0.9951 – 0.0485 = 0.9466
3.12 Draw pictures. a. z = 1.28, so the area is 1.0000 – 0.8997 = 0.1003.
b. z = 1.28, z = 2.56, so 0.9948 – 0.8997 = 0.0951.
3.13 Draw pictures and remember that you’re using the “backwards normal” method. Be sure
that you can tell why you need that backwards normal calculation from the statement of the
problem.
MATH 1342 BPS 5th ed.
HW Ch.3 notes
Send corrections / comments to Mary Parker at mparker@austincc.edu
last updated 09/10//09
page 2 of 3
3.14. Again, it is crucial to notice here and with all problems in the rest of this chapter how to
tell from reading the problem whether you will need to use the normal table “forward” or
“backward.” Learn to tell that from the statement of the problem. Pay attention to the difference
between problems like this problem and problems 3.11 and 3.12. Notice how the difference in
what is requested leads to a different method of approach to the problem.
What percentile is the median? Answer: 50% of the scores are below the median.
What percentile is the first quartile? Answer: 25th percentile.
What about the third quartile? Answer: 75% of the scores are below this.
Answers: the z-scores are 0 for the area of 50% below, -0.67 for the area of 25% below and
+0.67 for the area of 75% below. So the answers for this distribution are mean±z*(stdev) so
those are 0.800, 0.7477 and 0.8523.
Relevant to 3.25. (After you answer 3.25, compare your answers with those of other students
and discuss them.)
Here’s a similar, but more complex, question and an answer: Sketch a density curve that has its
peak at 0 on the horizontal axis but has a greater area within 0.25 on either side of 1 than within
0.25 of 0.
Answer: Various density curves would fit this. Here is one such density curve.
3.27 – 3.45. Make a picture for each. Follow the same ideas as you did for the problems in the
early part of the chapter.
3.47. In Chapter 10, we’ll learn more about this idea of approximating a distribution by a normal
distribution. Here, you are asked to do the exact calculations for this distribution in parts a and
b, and then, in part c, notice that the normal approximation is close to these, and in between the
two values, which it should be.
3.49. This is an important summary problem. Please think carefully about all parts of it.
a. It is very easy to use software to make the histogram. It is tedious to make the histogram by
hand. Make sure that you understand how to do it both ways.
b. It is convenient to use software to find the summary statistics. Be sure that you understand
which of them you’ll be required to do by hand on tests. The most important part of this
problem is the interpretation about the distances of the quartiles from the median. Ask about
this if it is not clear to you.
c. A very common way of assessing whether data fit a normal distribution is to do a computation
like the one asked for in this part of the problem. That is, to compare the percentage of scores in
the data that are between two points with the percentage of scores in a theoretical normal
distribution between the two corresponding points. Here are typical computations to do:
MATH 1342 BPS 5th ed.
HW Ch.3 notes
Send corrections / comments to Mary Parker at mparker@austincc.edu




last updated 09/10//09
page 3 of 3
What percentage in the data are between the 25th and 75th percentiles. In a theoretical
normal distribution, with no roundoff error, that would be 50%. How close is it in the
data?
What percentage in the data are between one standard deviation below the mean and one
standard deviation above the mean? In a theoretical normal distribution, with no
roundoff error, that would be about 68%. How close is it in the data?
What percentage in the data are between two standard deviations below the mean and two
standard deviations above the mean? In a theoretical normal distribution, with no
roundoff error, that would be about 95%. How close is it in the data?
What percentage in the data are between three standard deviations below the mean and
three standard deviations above the mean? In a theoretical normal distribution, with no
roundoff error, that would be about 99.7%. How close is it in the data?
3.52. This applet is useful to help you focus on the picture of the normal distribution and the
relationship between the scores in the distribution and the areas.