Download ExamView - Chapter 2 Practice Test.tst

Name: ________________________ Class: ___________________ Date: __________
ID: A
AP Stats Chapter 2 Practice Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Which of the following properties is true for all Normal density curves?
I. They are symmetric.
II. The curve reaches its peak at the mean.
III. 95% percent of the area under the curve is within one standard deviation of the mean.
A. I only
B. II only
C. I and II only
D. I and III only
E. All three statements are correct.
____
2. Which of these variables is least likely to have a Normal distribution?
A. Annual income for all 150 employees at a local high school
B. Lengths of 50 newly hatched pythons
C. Heights of 100 white pine trees in a forest
D. Amount of soda in 60 cups filled by an automated machine at a fast-food restaurant
E. Weights of 200 of the same candy bar in a shipment to a local supermarket
____
3. Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score
when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean
score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game
once, and they will compare z-scores. Jack gets a score of 14,000 and Jill gets a score of 16,000. Who won
the contest?
A. Jack
B. Jill
C. Nobody won.
____
4. A fire department in a rural county reports that its response time to fires is approximately Normally
distributed with a mean of 22 minutes and a standard deviation of 11.9 minutes. Approximately what
proportion of their response times is over 30 minutes?
A. 0.03
B. 0.21
C. 0.25
D. 0.75
E. 0.79
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Name: ________________________
ID: A
____
5. Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a Normal
distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. The percent of bags that will
contain between 16.0 and 16.1 ounces is about
A. 10
B. 16
C. 34
D. 68
E. None of the above is correct.
____
6. Below is a cumulative relative frequency graph for the 48 racers who finished the grueling 50km
cross-country ski race at the 2010 Vancouver Olympics. Approximately what proportion of the racers
finished the race in more than 2.15 hours?
A.
B.
C.
D.
E.
____
0.17
0.40
0.45
0.50
0.55
7. The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a
standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the
students will complete the exam in the time given?
A. 61.6 minutes
B. 78.4 minutes
C. 79.8 minutes
D. 84 minutes
E. 92.8 minutes
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Name: ________________________
ID: A
Short Answer
Scenario 2-1
Below is a cumulative relative frequency graph for the length of time a group of 62 students spent on a
no-time-limit final exam in Algebra II.
1. Use Scenario 2-1. What are the median and interquartile range for the amount of time these students spent on
the exam? Draw lines on the graph to show how you arrived at your answers.
.
2. Use Scenario 2-1. According to these data, the mean time students spent on the exam was 94.1 minutes, and
the standard deviation was 24.23 minutes. Suppose the exam proctor realized after compiling these data that
he had used the wrong start time in his calculation, so that each value for time spent on exam needs to be
reduced by 15 minutes. He also wants to express the times in hours, rather than minutes. Find the mean and
standard deviation of the transformed data.
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Name: ________________________
ID: A
Scenario 2-2
A real estate company compiled data on the prices at which 35 homes sold during a one month in a county in
New Jersey. A histogram and some summary statistics from Minitab for the home prices are given below.
(Note that home prices are in thousands of dollars.)
Descriptive Statistics: home prices
Variable
Home
Prices
N
35
Mean
260.8
SE Mean
24.6
StDev
145.6
Minimum
80.0
Q1
165.0
Median
220.0
Q3
307.0
Maximum
626.0
3. Use Scenario 2-2. On the axes below, make a rough sketch of a density curve for these data, based on the
histogram above. How would you describe the shape of this density curve?
4. Use Scenario 2-2. One of the houses in this data set sold for 350 thousand dollars. Six houses sold for more
than that. Calculate and interpret the percentile and z-score for this house’s price.
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ID: A
AP Stats Chapter 2 Practice Test
Answer Section
MULTIPLE CHOICE
1. ANS: C
/C/Correct! All Normal curves are symmetric and peak at the mean, but 95% of the area is within 2 standard
deviations of the mean, not 1.
PTS: 1
REF: Test 2A
2. ANS: A
/A/Correct! Annual income in any company is likely to be skewed right, with upper level administrators on
the right tail. The other four variables are more likely to be Normal.
PTS: 1
REF: Test 2C
3. ANS: A
/A/Jack’s z = 1.07 and Jill’s z = 0.90; Jack wins the contest.
PTS: 1
4. ANS: C
/C/Correct!
REF: Test 2B
of the times are above that value.
, which is the 75th percentile of the Standard Normal curve, so about 25%
PTS: 1
REF: Test 2A
5. ANS: C
/C/Correct! By the 68-95-99.7 rule, 68% of the scores are within 1 standard deviation from the mean. The
area from 16.0 to 16.1 is exactly half of this area (just the half below the mean).
PTS: 1
REF: Test 2B
6. ANS: C
/C/Correct! Using the graph, cumulative relative frequency for 2.15 is approximately 0.55, so
1 – 0.55 = 0.45 of the time were longer than 2.15.
PTS: 1
REF: Test 2B
7. ANS: B
/B/ Correct! Using table A, look up the proportion .80 inside the areas to find the z-score. The z-score will be
0.84. Then set up the following equation to find the time:
x = 78.4 minutes
PTS: 1
TOP: Inverse Normal Calculations
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ID: A
SHORT ANSWER
1. ANS:
Median is approximately 95 minutes. The interquartile range is approximately 110 – 75 = 35 minutes.
PTS: 1
REF: Quiz 2.1B
TOP: Describing Location in a Distribution
2. ANS:
Mean = (94.1 – 15)/60 = 1.318 hours, standard deviation = 24.23/60 = 0.404 hours.
Transforming Data: Subtracting a costant will change the center but not the spread.
PTS: 1
REF: Quiz 2.1B
TOP: Describing Location in a Distribution
3. ANS:
The density curve should be skewed to the right!!! This distribution is not normal.
PTS: 1
REF: Quiz 2.1B
TOP: Describing Location in a Distribution
4. ANS:
The house that sold for $350 thousand has 28 out of 35 house prices below it and 6 above it, so it is at the
80th percentile (28/35). Interpretation: The 80th percentile means that 80% of houses sold less than $350,000.
The z-score for $350 thousand is (350 – 260.8)/145.6 = 0.61, which is 0.61 standard deviations above the
mean house price.
PTS: 1
REF: Quiz 2.1B
TOP: Describing Location in a Distribution
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