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AP Stats chapter 1 & 2

Total questions: 57

Worksheet time: 2hrs 54mins

Name
Class
Date
1.

The area under the standard normal curve corresponding to -0.2 < z < 2.03 is

a)

0.5581

b)

0.5686

c)

0.3995

d)

0.4100

2.

The scores of the math portion of the SAT are approximately normal with a mean of 510 and a standard deviation of 42. Approximately what percent of students will score higher than 600?

a)

0.9838

b)

0.0162

c)

0.0179

d)

0.9821

3.

The life span of ladybugs is approximately normally distributed with a mean of 18 months and a standard deviation of 2.5 months. Only about 5% of ladybuds will have a lifespan outside which interval?

a)

15.5 to 23 months

b)

15.5 to 20.5 months

c)

13 to 23 months

d)

10.5 to 25.5 months

4.

The average high temperature in July for a midwest city is 89 degrees. What is the standard deviation if 15% of July's on record for the city have an average high temperature above 91.5 degrees? Assume average temperatures are normally distributed.

a)

s = 0.060

b)

s = 16.667

c)

s = 0.416

d)

s = 2.404

5.

95% of students who take the AP stats exam need between 186 and 214 minutes to complete it. What is the standard deviation of time students need to finish the exam? Assume times are normally distributed.

a)

4.67 minutes

b)

14 minutes

c)

7 minutes

d)

28 minutes

6.

Suppose that the mean of a set of values is 20, and the standard deviation is 3. If each value is increased by 5, what will be the mean and standard deviation of the new set of values?

a)

mean = 25, sd = 8

b)

mean = 20, sd = 3

c)

mean = 20, sd = 8

d)

mean = 25, sd = 3

7.

A college offers scholarships to students who score in the top 2% of students on an entrance exam. If the mean score on the exam is 176 and the standard deviation is 4, what is the minimum score a student would need to get a scholarship?

a)

167.80

b)

184.20

c)

176.08

d)

179.92

8.

The EPA requires that the exhaust of each model of motor vehicle be tested for the level of several pollutants. The level of oxides of nitrogen (NOX) in the exhaust of one light truck model was found to vary among individual trucks according to an approximately Normal distribution with mean μ = 1.45 grams per mile driven and standard deviation σ = 0.40 gram per mile. Which of the following best estimates the proportion of light trucks of this model with NOX levels greater than 2 grams per mile?

a)

0.0228

b)

0.0846

c)

0.4256

d)

0.9154

e)

0.9772

9.

When Sam goes to a restaurant, he always tips the server $2 plus $10% of the cost of the meal. If Sam's distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of his tip distribution?

a)

$2.90, $0.30

b)

$2.90, $2.30

c)

$9.00, $3.00

d)

$11.00, $2.00

e)

$2.00, $0.90

10.

Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 21 and standard deviation 5. Wayne's standardized score on the ACT was -0.6. What was Wayne's actual ACT score?

a)

3

b)

13

c)

16

d)

18

e)

24

11.
a)

The median is at the yellow line and the mean is at the red line

b)

The median is at the red line and the mean is at the yellow line

c)

The mode is at the red line and the median is at the yellow line

d)

The mode is at the yellow line and the median is at the red line

e)

The mode is at the red line and the mean is at the yellow line

12.

A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. Based on this report, what is the approximate standard deviation of weight for this species of cockroaches?

a)

4.6

b)

5.0

c)

6.2

d)

4.0

e)

Cannot determine without more information

13.

Suppose that the distance a golfer can hit the ball has an approximately normal distribution with a mean of 250 yards and a standard deviation of 10 yards.


What proportion of his hits will travel between 215 and 255 yards?

a)

0.3088

b)

0.65

c)

0.6912

d)

0.7641

e)

0.95

14.

Suppose that the distance a golfer can hit the ball has an approximately normal distribution with a mean of 250 yards and a standard deviation of 10 yards.


The highest 20% of his hits will travel at least what distance?

a)

241 yards

b)

249 yards

c)

258 yards

d)

262 yards

e)

265 yards

15.

What is the approximate standard deviation of the following Normal distribution?

a)

1

b)

3

c)

7

d)

9

e)

10

16.

The dotplot to the right shows the number of home runs for a random sample of 50 baseball players in the 2014 season. The mean of this distribution is 3.32 homeruns and  σ=5.89\sigma=5.89  homeruns.


Canyon del Oro alumni Ian Kinsler is represented by the dot at 13 homeruns.  At what percentile is Kinsler?

a)

8th percentile

b)

26th percentile

c)

50th percentile

d)

74th percentile 

e)

92nd percentile

17.

The dotplot to the right shows the number of home runs for a random sample of 50 baseball players in the 2014 season. The mean of this distribution is 3.32 homeruns and  σ=5.89\sigma=5.89  homeruns.

If each of these 50 values was standardized, what would be the best description of the resulting distribution of standardized scores.

a)

Exactly Normal with mean = 0 and SD = 1

b)

Approximately Normal with mean = 0 and SD = 1

c)

Approximately Normal with mean = 3.32 and SD = 5.89

d)

Skewed right with mean = 0 and SD = 1

e)

Skewed right with mean = 3.32 and SD = 5.89

18.

In a standard Normal distribution, what proportion of the values are less than 0.54?

a)

0.2946

b)

0.7054

c)

0.0778

d)

0.9222

e)

This cannot be determined without the mean and standard deviation.

19.

If I tell you that you scored at the 55th percentile on your final exam, you would know:

a)

55% of the class scored the same or worse than you did

b)

You earned a 55% on the exam

c)

You failed the exam

d)

45% of the class scored worse than you did

20.

The Median is also referred to as

a)

the 25th Percentile

b)

the 50th Percentile

c)

the 75th Percentile

d)

the 100th Percentile

21.

The z-score represents.....

a)

the amount of standard deviations a data value is above or below the mean.

b)

the percentile the data value is above or below the mean.

c)

the amount of standard deviations a data value is above or below the median.

d)

the percent the data value is above or below the median.

22.

What is the purpose of z-scores?

a)

to describe the exact location of a score within a distribution

b)

to find the mean of the distribution

c)

to describe the shape of the distribution

d)

to find the standard deviation of the distribution

23.

The mean test score for a class was 76 with a standard deviation of 5 points, and the shape was skewed left. The teacher decides to add 4 points to every students test score. What is the new mean, standard deviation, and shape for the distribution of test scores?

a)

mean=80, SD=5, shape is skewed left

b)

mean=80, SD=9, shape is skewed left

c)

mean=80, SD=5, shape is more skewed left

d)

mean=80, SD=9, shape is approx. symmetric

24.

A 50 point test had a mean of 42 with a standard deviation of 5 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100). What is the new mean, standard deviation and shape for the distribution of test scores?

a)

mean=84, SD=10, approx. symmetric

b)

mean=84, SD=5, approx. symmetric

c)

mean=42, SD=5, approx. symmetric

d)

mean=84, SD=10, slightly skewed right

25.

A 50 point test had a mean score of 39 with a standard deviation of 4 points. The original shape of the distribution of test scores was approximately symmetric. The teacher decides to multiply all scores by 2 (so the total is out of 100) and then also add 3 points. What is the new mean, standard deviation and shape for the distribution of test scores?

a)

mean=81, SD=8, approx. symmetric

b)

mean=81, SD=11, approx. symmetric

c)

mean=78, SD=8, approx. symmetric

d)

mean=81, SD=4, approx. symmetric

26.

What is the median age?

a)

60

b)

55

c)

50

d)

45

27.

What percent of the college students surveyed have less than $2000 in debt?

a)

25%

b)

50%

c)

75%

d)

100%

28.

If the heights of a population of women follow a Normal distribution, and 99.7% have heights between 4′0″ and 6′0″, what is your estimate of the standard deviation of the heights in this population?

a)

1 inch

b)

4 inches

c)

6 inches

d)

12 inches

29.

What is the total area under the normal curve in a standard normal distribution?

a)

1

b)

2

c)

3

d)

4

30.
The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds.  What is the z-score for a player who runs a time of 5.6 seconds?
a)
-1.33
b)
1.33
c)
0.88
d)
1.02
31.
In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval? 
a)
1084 to 1216 pounds 
b)
1106 to 1150 pounds 
c)
1106 to 1194 pounds 
d)
1128 to 1172 pounds
32.

A statistical study calculated that the average cost of used iPhones is $230, with a standard deviation of $25. What is the probability that a select phone from the sample costs between $224 and $268?

a)

0.5306

b)

0.4694

c)

0.9608

d)

0.3409

33.
a)

A

b)

B

c)

C

d)

D

e)

E

34.
a)

A

b)

B

c)

C

d)

D

e)

E

35.
a)

A

b)

B

c)

C

d)

D

e)

E

36.
a)

A

b)

B

c)

C

d)

D

e)

E

37.
a)

A

b)

B

c)

C

d)

D

e)

E

38.
a)

A

b)

B

c)

C

d)

D

e)

E

39.
a)

II only

b)

I and II

c)

I and III

d)

II and III

e)

I, II, and III

40.
a)

A

b)

B

c)

C

d)

D

e)

E

41.
a)

A

b)

B

c)

C

d)

D

e)

E

42.
a)

A

b)

B

c)

C

d)

D

e)

E

43.
Here is the dot plot of voter turnout (as a percentage of voting-age population) for the 50 states—plus the District of Columbia—in a recent presidential election. Which of the following best describes this distribution?
a)
The distribution of voter turnout is skewed slightly left, centered at about 62%, with a range of 24%.
b)
The distribution of voter turnout is roughly symmetric, centered at about 60%, with a range of 30%.
c)
The distribution of voter turnout is skewed slightly right, centered at about 62%, with a range of 24%.
d)
The distribution of voter turnout is bimodal, centered at about 60%, with a range of 30%.
44.
The stem-and-leaf diagram below gives the distribution of the ages in years of 20 participants at a family reunion. Which of the following statements about the distribution is correct?
a)
The first quartile is larger than the third quartile.
b)
The distribution is strongly skewed to the left.
c)
It makes the most sense to use the mean and standard deviation as a numerical summary of the center and spread of this distribution.
d)
The mean is larger than the median.
45.
Independently selected groups of middle-school children were given a poem to memorize. After a certain period of time, they were asked to recall as much of the poem as they could. A back-to-back stem plot of the distribution of the number of words that each group of children could correctly remember is displayed above. Which of the following statements about these data is true?
a)
There are more students in Group 1 than in Group 2.
b)
The third quartile of the Group 1 distribution is larger than the maximum value of the Group 2 distribution (that is, 25% of the Group 1 values are larger than any Group 2 value).
c)
The median of the Group 2 distribution is smaller than the first quartile of the Group 1 distribution (that is, 50% of the Group 2 values are smaller than at least 75% of Group 1 values).
d)
The mean number of words remembered for Group 1 is smaller than the mean number of words remember for Group 2.
46.
The side-by-side boxplots show the distribution of test scores in Ms. Williams’s two sections of calculus. Based on these boxplots, which one of the following statements must be true?
a)
The lowest score in A period was close to the 15th percentile of the C period class.
b)
The mean score for students in C period was higher than the mean score for students in A period.
c)
More people scored between 72 and 90 in C period than scored between 72 and 81 in A period.
d)
The standard deviation of scores in A period is smaller than the standard deviation of scores in C period.
47.
In which of the following situations would a pie chart be an appropriate graph to use to summarize your data?
a)
You want to display the distribution of favorite color for the students in your statistics class.
b)
You want to compare the percentages of students in each grade at your school who favor a certain candidate for school president.
c)
You want to compare the life expectancies of different professions by displaying and comparing graphs of ages at death for random samples of famous scientists, authors, actors, and politicians.
48.
Which of the distributions displayed in the dot plots below has the highest standard deviation?
a)
Distribution A
b)
Distribution B
c)
Distribution C
49.
According to the 1.5 x IQR rule, how many outliers are there in the data set 72, 110, 114, 115, 118, 123, 144, 156?
a)
None
b)
One
c)
Two
d)
Three
50.
The histogram shows the typical travel time to school (self-reported) for 50 high school students. Which of the following statements is true about the mean and median of this distribution?
a)
Mean > Median
b)
Mean < Median
c)
Mean = Median
d)
Mean ≈ Median
51.
A zoologist studying adult bears measures a number of different variables. Which of the possible variables is categorical (qualitative)?
a)
the weight in pounds of an adult bear
b)
the level of aggression (low, moderate, high) displayed by an adult bear
c)
the number of fish an adult bear eats in a particular day
52.
Jerome’s summer reading list has 8 books, and he is examining the number of pages in each book. After calculating the mean, median, standard deviation, and interquartile range, he realized that the longest book is actually 100 pages longer than he thought it was. Which of his measurements does he need to recalculate?
a)
All his measurements.
b)
The mean, standard deviation, and interquartile range.
c)
The mean and standard deviation.
d)
Only the mean.
53.
An adult male aged 20-29 who is 73 inches tall would be shorter than what percent of males in his age group?
a)
10%
b)
15%
c)
85%
d)
90%
54.
Sally was so excited after collecting her data that she slipped and fell in the mud! She can no longer read her data but she knows the median is 35.4 inches with a range of 12 inches. Sally also realizes that she needs to add 1 inch to all her measurements because of a faulty ruler, then convert everything to feet. What would her median and range be after making these adjustments?
a)
Median = 3.033 feet
Range = 1.083 feet
b)
Median = 3.033 feet
Range = 1 foot
c)
Median = 2.95 feet
Range = 1.083 feet
d)
Median = 2.95 feet
Range = 1 foot
55.

A random sample of 50 students reported their gender, then selected from 4 options of one word that best described how they felt at the time. The results are summarized in the table. What percentage of males felt tired?

a)

1.2 %

b)

12.0%

c)

24.0%

d)

54.5%

e)

57.1%

56.

The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. What is wrong with the way information is presented in this graph?

a)

There should be a title and a variable label on the horizontal scale.

b)

The vertical scale should begin at 0 so the Chevrolet bar doesn't look disproportionately larger than Ford and Toyota.

c)

The vertical scale should have been measured in number of owners satisfied instead of percent of owners satisfied.

d)

This information should have been displayed in a pie chart.

57.

Suppose we classify 315 randomly selected college students according to their general major field and their self-described political viewpoint. The table presents the results. Which of the following characteristics of these data supports the conclusion that there is an association between political viewpoint and general major field?

a)

A higher proportion of students with a liberal political viewpoint major in the humanities, and a higher proportion of moderates and conservatives major in business.

b)

The marginal distributions of the two variables are not proportional.

c)

A similar proportion of students who major in humanities and who major in social sciences have a liberal political viewpoint.

d)

The sample does not contain equal number of individuals in each category.

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