Mathematics IV Study Guide
Fall 2013
Henry County Schools
In Addition to these sample problems, students should review
all previous test questions, class notes, and formative and
summative assessments, etc. in preparation for this Exam
Part I: Unit 2 (Sequences) Wednesday
Part II: Unit 3 (Rational Functions) Thursday
Part III: Unit 1 (Data Analysis) Friday
Z-Score Table
Z-Score Table
c
0.50
0.60
0.70
0.80
0.90
0.95
0.96
0.98
0.99
0.995
0.998
0.999
zc
0.674
0.841
1.036
1.282
1.645
1.960
2.053
2.326
2.576
2.807
3.090
4.500
Calculator Cheat Sheet for Math IV – Unit 1 Assessment
Students may use on assessment
Finding confidence interval
with a calculator if you know
x, Sx , n, and c  level






Stat
Tests
8
Stats
Enter (stats must be
highlighted)
Enter
Finding confidence interval
without a calculator:
Margin of Error:
E  zc 
xE    xE
Sx
n
x, Sx , n, and c  level


Enter twice
Confidence interval in
parentheses
Putting data into the
calculator:


Stat
1
Calculating
x, S x , n, min X , Q1 , Med ,
Q3 and max X





Stat
Calc
1
Enter
Generating a random
sample in a list (L1)



Stat
1





L1 (should be highlighted)
MATH
PRB
5
randInt(13, 18, 10)
Lowest
number
Highest
number
Sample
size
MM4D1: Using simulation, students will develop the idea of the central limit
theorem.
Simulating and Describing Data
For problems 1 – 2 simulate collecting data by finding a random set of integers
with the given parameters. Plot the sample set on a dot plot and describe the
distribution of the data.
1. Twenty integers between 10 and 15, inclusive
___________________________________________________________________________________
dot plot
2. Thirty integers between 20 and 30, inclusive
__________________________________________________________________________________
dot plot
3. A random set of integers is generated to simulate a data collection of integers from
50 to 55. Which set of data that follows could be the generated integers?
a. { 50, 51, 51, 52.5, 55}
b. { 51, 53, 55, 55, 56}
c. {53, 54, 55, 55, 56}
d. {54, 54, 54, 55, 55}
4. A sample of 100 data points is collected. The data is skewed to the left. Twenty
more samples of data are collected, each with 100 data points. What is the
distribution of all the data points?
a. Normal
b. Skewed to the left
c. Skewed to the right
d. Distribution is not certainly known
5. State the central limit theorem:
_______________________________________________________________________________________________
_______________________________________________________________________________________________
_______________________________________________________________________________________________
_______________________________________________________________________________________________
6. Which data set has a distribution that is skewed to the left?
a.
b.
c.
d.
{1, 2, 3, 3, 3, 3, 3, 3, 4, 5}
{14, 15, 15, 15, 16, 16, 17, 18, 21}
{25, 25, 26, 27, 28, 29, 29, 30, 31}
{32, 36, 38, 40, 41, 42, 43, 43, 44}
MM4D2: Using student-generated data from random samples of at least 30
members, students will determine the margin of error and confidence interval
for a specified level of confidence.
7. What is the margin of error of the mean of 50 data items with a standard deviation
of 3.2? Use a confidence level of 90%.
a. 0.11
b. 0.23
c. 0.74
d. 37.22
8. Determine the confidence interval, for a 95% confidence level, of the population
mean for a set of data with a margin of error 1.9 and a sample mean of 18.3.
a. -1.9 < m < 1.9
b. 16.4 < m < 20.2
c. 17.4 < m < 19.2
d. -16.4 < m < 20.2
9. What is the mean and standard deviation of the data set below?
35
48
27
36
16
23
37
37
40
42
42
17
32
39
34
39
36
23
19
47
45
25
20
30
44
46
35
17
25
24
17
47
46
24
41
37
45
29
36
37
Mean = _____________________
Standard deviation = __________________________
10. What is the margin of error of the mean of 60 data items with a standard deviation
of 1.4 and mean of 10.4? Use a confidence level o f99%.
a. 0.060
b. 0.465
c. 9.935
d. 130.58
11. A set of data items with which confidence level and corresponding z-score would
have a margin of error of 0.8375? The sample standard deviation is approximately
3.6.
a. 90%; zc = 1.645
b. 95%; zc = 1.96
c. 90%; zc = 1.645
d. Cannot be determined
MM4D3: Students will use confidence intervals and margins of error to make
inferences from data about a population. Technology is used to evaluate
confidence intervals, but students will be aware of the ideas involved.
12. What is the confidence interval for the population mean if the sample mean is 36.15,
the sample standard deviation is 0.98, and the confidence level is 91%? There are
90 items in the sample data set.
a. 35.17 < m < 37.13
-0.18 < m < 0.18
c. 32.90 < m < 39.40
d. 35.97 < m < 36.33
b.
13. A random selection of 200 wedding photographers was surveyed throughout the
United States. The photographers were asked the base hourly rate they charged to
photograph a wedding. With 92% confidence, the confidence interval of the
population mean of the data was 98.10 < m <142.30 . Which statement that follows
could be reasonably assumed of all wedding photographers in the United States?
a. With 92% confidence, a wedding photographer will charge at least $98.00
per hour.
b. With 92% confidence, the hourly rate of a wedding photographer will range
between $98.10 and $142.30.
c. No wedding photographers charge more than $142.30 per hour.
d. All wedding photographers charge at least $98.10 per hour.
14. Which can be inferred about the population mean if the margin of error is 0.113, the
sample mean is 4.2, the standard deviation is 0.51, the sample size is 55, and the
confidence level is 90%?
a. No more than 90% of the 55 data points are within 0.51 units of 4.2
b. It is 90% probable that the population mean is equal to 4.2
c. With 90% confidence, the population standard deviation is 0.51.
d. With 90% confidence, the population mean is between 4.09 and 4.31.
15. What is the confidence interval for the population mean if the sample mean is
36.15, the sample standard deviation is 0.98, and the confidence level is 91%?
There are 90 items in the sample data set.