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Statistics Final Exam

Total questions: 69

Worksheet time: 1hrs 20mins

Name
Class
Date
1.
A bag contains 5 green marbles, 7 blue marbles and 3 yellow marbles. Find the probability of selecting a green marble from the bag.
a)
1/5
b)
1/3
c)
7/15
d)
2/3
2.
What is the probability of selecting a cherry piece?
a)
3/12
b)
12/12
c)
5/12
d)
4/12
3.

A dice is rolled. What is the probability that the result is less than 3?

a)

1/2

b)

1/3

c)

1/4

d)

1/6

4.
What is the likelihood of picking a black card from a standard deck of playing cards?
a)
13/52
b)
4/52
c)
26/52
d)
8/52
5.
In a standard deck of 52 playing cards, what is the probability that a randomly chosen card is a red 7?
a)
3/52
b)
4/52
c)
2/52
d)
13/52
6.
The spinner is spun until it lands on one of the five edges of the pentagon. What is the probability that the number it lands on is odd?
a)
1/5
b)
2/5
c)
1/2
d)
3/5
7.
The theoretical probability of rolling 4 with two dice is 3/36. How many 4s would you expect to roll if you rolled a set of two dice 100 times?
a)
About 3
b)
About 10
c)
About 30
d)
About 100
8.
Which of the following situations is represented by this tree diagram?
a)
3 shirt options, 6 pants options, and 12 shoe options
b)
3 shirt options, 2 pants options, and 2 shoe options
c)
2 shirt options, 3 pants options, and 1 shoe option
9.

You spin this spinner 3 times. Find the probability of spinning a red first, odd second, and a 3 on the last spin.

a)

1/216

b)

1/72

c)

1/36

d)

1/12

10.
Probability can be between what two numbers?
a)
10 and 20
b)
0 and 100
c)
0 and 1
d)
All Numbers are possible
11.
a)
.2855
b)
.6246
c)
.0922
d)
.3230
12.
A bag contains 5 red marbles and 4 pink marbles. A marble is randomly drawn and then replaced. What is the probability the first marble is pink and the second is red?
a)
26.9%
b)
24.7%
c)
20.0%
d)
5%
13.
A bag contains 5 red marbles and 4 pink marbles. A marble is randomly drawn and does not get replaced. What is the probability that both marbles are red?
a)
27.8%
b)
24.7%
c)
20.0%
d)
4%
14.

Amber rolls two dice and it is known that the sum of the numbers is 7. What is the probability one die is a 5? That is, what's the chance of selecting an outcome that contains a 5 when you restrict to only those outcomes that add up to 7?

a)

16.7%

b)

19.8%

c)

33.3%

d)

8.3%

15.
What term refers to the set of all possible outcomes?
a)
Sample Space
b)
Probability
c)
Probability Distribution
d)
Tree Diagram
16.
The mathematical quantity Σx P(x) yields a number referred to by what two names?
a)
Expected Value, Mean
b)
Expected Value, Sum
c)
Mean, Probability Distribution
d)
Mean, Sigma
17.
What term refers to the situation where two events have no elements in common?
a)
Disjoint
b)
Independent
c)
Disconnected
d)
Venn Diagram
18.
What is the probability of flipping at least two heads flips from 5 total coin flips? Assume that a fair coin is used.
a)
26/32
b)
2/32
c)
6/32
d)
8/32
19.

In a normally distributed data distribution with a mean of 100 and a standard deviation of 10, what is the 75th percentile?

a)

106.7448975

b)

110

c)

108.6271843

d)

112

20.

In a normally distributed data distribution with a mean of 100 and a standard deviation of 10, what is the z-score that corresponds to the 90th percentile?

a)

1

b)

2

c)

1.281551567

d)

1.682163271

21.

In a normally distributed data distribution with a mean of 100 and a standard deviation of 10, what is the interval centered around the mean in which 60% of all observations will fall?

a)

(91.58, 108.42)

b)

(90, 110)

c)

102.53

d)

(89.12, 111.84)

22.

In a normally distributed data distribution with a mean of 100 and a standard deviation of 10, what is the probability that a randomly selected observation will be greater than 120?

a)

.022750062

b)

.977249938

c)

.036581264

d)

.963418736

23.

For a normally distributed data set, what is the probability that an observation is at least 2.2 deviations away from the mean? [You might begin by drawing a normal curve with a center between the endpoints z=-2.2 and z=2.2.]

a)

2 x 0.0139

b)

2 x 0.0212

c)

2 x 0.0176

d)

.9722

24.

Given a normally distributed data distribution, such as heights of a large population, suppose that a particular height is the 75th percentile. What would be the corresponding z-score for this height?

a)

1

b)

.6744897495

c)

Not possible to determine

d)

.8151624982

25.

Suppose you play a $2 scratch off game where there is a 1 in 4 chance to win $2, a 1 in 10 chance to win $10, a 1 in 15 chance to win $250, and a 1 in 25 chance to win $5000. What is the expected value if X represents net winnings, i.e., winnings minus cost per ticket?

a)

216.17

b)

200.17

c)

-216.17

d)

127.37

26.
Suppose an exam has an average of 59 and a standard deviation of 11. Assume the scores are approximately normally distributed. What is the approximate exam score for which only 18% scored higher?
a)
69.07
b)
72.12
c)
55.67
d)
75.54
27.
What is the positive z-score for which 28% of normally distributed data will fall within z deviations of the mean? Also, if μ = 68 and σ = 11, then what number corresponds to z?
a)
.358, 71.943
b)
.401, 74.826
c)
.319, 68.394
d)
.396, 73.012
28.
Suppose you flip two coins and roll one standard six sided die. How many elements are there in the sample space?
a)
24
b)
12
c)
48
d)
36
29.

Suppose a restaurant finds its daily profits have a normal distribution with mean $140 and standard deviation $80. What is the probability that the restaurant loses money on any given day? That is, what is the probability that the profit is less than $0?

a)

0.04

b)

0.1

c)

0.015

d)

0.075

30.
What word refers to our best guess for the parameter?   
a)
Confidence Interval
b)
Confidence Level
c)
Point Estimate
d)
Margin of Error
31.

What is the z-score that corresponds to a 99% confidence interval?

a)

2.62

b)

2.58

c)

2.68

d)

2.72

32.

What is the z-score that corresponds to a 96% confidence interval?

a)

2.58

b)

1.75

c)

2.05

d)

1.96

33.

If 1757 represents "yes" voters out of 2584, what would be our appropriate point estimate for the proportion of yes voter in the whole population?

a)

.6799535604

b)

.3200464396

c)

1.96

d)

.0091769818

34.

If 1757 represents "yes" voters out of 2584, what would be our appropriate standard error for the proportion of yes voter in the whole population?

a)

.6799535604

b)

.3200464396

c)

1.96

d)

.0091769818

35.

If 1757 represents "yes" voters out of 2584, construct a 95% confidence interval for the "yes" group.

a)

(.662, .698)

b)

(.302, .338)

c)

(.305, .335)

d)

(.665, .695)

36.

If 1757 represents "yes" voters out of 2584, construct a 95% confidence interval for the "no" group.

a)

[.662,.698]

b)

[.298,.342]

c)

[.302,.338]

d)

[.288,.352]

37.
Suppose 544 females were surveyed. It as determined that the median ideal number of children is 2, the mean is 3.09, and the standard deviation is 1.19. Find the 95% confidence interval.
a)
[2.98,3.19]
b)
[2.92,3.26]
c)
[3.00,3.36]
d)
[1.19,3.19]
38.

The heights of 6 plants are 54.6, 59.6, 61.6, 62.4, 64.9, and 70.6. What would be an appropriate point estimate for a population of plants to which these plants belong?

a)

65

b)

64.2

c)

59.1

d)

62.3

39.
If a set has a population proportion of .6 and a sample size n=6, what's the standard deviation of the sampling distribution?
a)
.3
b)
.14
c)
.2
d)
.42
40.

What is the t-score that corresponds to a 95% confidence interval with a sample size of n = 20?

Skip this since we didn't get to this content.

a)

2.093

b)

1.96

c)

2.58

d)

2.086

41.

Find the margin of error for a 95% confidence interval when the sample standard deviation equals 90 and n = 400. Recall that the margin of error is the amount you add and subtract from the point estimate when calculating a confidence interval.]

Skip this since we didn't get to this content.

a)

8.65

b)

8.85

c)

7.87

d)

9

42.

This statistical object contains the most plausible values for the parameter.

a)

Confidence Interval

b)

Confidence Level

c)

Point Estimate

d)

Margin of Error

43.

The mean and standard deviation of a population are 200 and 20, respectively, and the sample size is 25.

What is the mean of the sampling distribution?

a)

200

b)

16

c)

25

d)

4

44.

The mean and standard deviation of a population are 200 and 20, respectively, and the sample size is 25.

What is the standard deviation of the sampling distribution?

a)

200

b)

16

c)

25

d)

4

45.

The mean and standard deviation of a population are 200 and 20, respectively. Assume that the population distribution is a normal distribution. What is the probability of randomly selecting an observation less than 190?

a)

69%

b)

42%

c)

31%

d)

58%

46.

The mean and standard deviation of a population are 200 and 20, respectively. What is the probability of randomly selecting a sample of 25 observations with a sample mean less than 190? [Assume that the sampling distribution is approximately normal.]

a)

69%

b)

0.6%

c)

31%

d)

99%

47.

A z-score tells you...

a)

the standard deviation of a sampling distribution.

b)

the original raw observation on which it is based.

c)

if the distribution it comes from is normal.

d)

how many standard deviations away from the mean an observation lies (above, below, or at).

48.

What is the standard deviation of the distribution if we assume that the nested areas centered about the mean are about .683, .995, and .997, respectively, and the curve is a normal distribution?

a)

1010

b)

20

c)

60

d)

1030

49.
Increasing the sample size of an opinion poll will reduce the
a)
bias of the estimates made from the data collected in the poll.
b)
variability of the estimates made from the data collected in the poll.
c)
variability of opinions in the sample.
d)
variability of opinions in the population.
50.
28% of all Woodrow students believe Monday will be snow day. You take a sample of 50 students and find that 15 of them believe Monday will be a snow day. What is the probability of getting a sample of size 50 that has 15 or more students who believe Monday will be a snow day? 
a)
0.376
b)
Cannot be determined because the distribution of the sample proportion of samples of size 50 is not normal
c)
0.624
d)
0.99999
51.
The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
What is the mean of the sampling distribution of p-hat?
a)
0.4
b)
0.44
c)
0.56
d)
0.6
52.
The Gallup Poll asked a random sample of 1785 adults whether they attended church during the past week.  Let p-hat be the proportion of people in the sample who attended church.  A newspaper report claims that 40% of all U.S. adults went to church last week.  Suppose this claim is true. 
Calculate the standard deviation of the sampling distribution.
a)
0.0116
b)
0.0117
c)
0.0118
d)
0.0119
53.

At a particular college, 78% of all students are receiving some kind of financial aid. The school newspaper selects a random sample of 100 students and 72% of the respondents say they are receiving some sort of financial aid. Which of the following is true?

a)

78% is a population and 72% is a sample.

b)

72% is a population and 78% is a sample

c)

78% is a parameter and 72% is a statistic

d)

72% is a parameter and 78% is a statistic

54.

Suppose you pay $1.00 to roll a fair die with the understanding you will get $3.00 back rolling a 2 or a 4, and nothing otherwise. What is the expected amount you will win on average per roll in the long run? [Remember LOLN]

a)

$0.00

b)

-$1.00

c)

$1.00

d)

$3.00

55.

You pick a card from a deck. If you get a face card, you win $5. If you get an ace, you win $30 plus an extra $60 for the ace of hearts. For any other card you win nothing. Find the expected value you will win on average per card draw in the long run. [Remember LOLN.]

a)

$5.00

b)

$3.85

c)

$4.04

d)

$4.62

56.
a)
Graph A
b)
Graph B
c)
Graph C
d)
Graph D
57.
a)
Graph A
b)
Graph B
c)
Graph C
d)
Graph D
58.
a)
Graph A
b)
Graph B
c)
Graph C
d)
Graph D
59.
a)
Graph A
b)
Graph B
c)
Graph C
d)
Graph D
60.
a)
2.872
b)
2.862
c)
2.031
d)
.642
61.
a)
2
b)
4
c)
25
62.
a)
2
b)
4
c)
25
63.
a)
Yes
b)
No
64.
a)
Yes
b)
No
65.
a)
All of them
b)
All but A
c)
All but A and D
d)
All but A, B, and D
66.

The lifetime of a certain type of battery is known to be normally distributed with a standard deviation of 20 hours. A sample of 50 batteries had a mean lifetime of 120.1 hours. It is desired to construct a 99% confidence interval for the mean lifetime of this type of battery.


What is the confidence interval to one decimal place?

a)

(114.5, 125.6)

b)

(112.8, 127.4)

c)

(112.82, 127.38)

d)

(114.56, 125.64)

67.
A research company wants to estimate the proportion of people who like oatmeal.  They want the confidence level to be 95%.  The company gets 325 people to sign up for the survey, but on the day that the survey is issued, only 250 people show up and take the survey.  What happens to the confidence interval?
a)
It gets larger
b)
It gets smaller
c)
It stays the same
d)
Too little information given
68.
A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?
a)
0.001 < p < 0.005
b)
0.566 < p < 0.693
c)
0.148 < p < 0.252
d)
0.023 < p < 0.045
69.

A study found that in a sample of 44 subjects, 9 of agree that children under 6 shouldn’t be taken to nice restaurants.


The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

a)

95% of the time the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8%.

b)

The population proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

c)

The probability that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants will be between 8.2% and 31.8% is 95%.

d)

Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn't be taken to nice restaurants is between 8.2% and 31.8%.

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