Deck 7: Theoretical Distributions Including the Normal Distribution

Question 1

If an urn contains 2 red balls, 2 blue balls, and 1 green ball, the probability of drawing a red ball is .50.

Answer 1

False

Question 2

Empirical distributions are based on mathematics and logic.

Answer 2

False

Question 3

The inflection points on the normal curve are at z = -1 and z = +1.

Answer 3

True

Question 4

A point on the normal curve with .35 of the curve beyond it has .15 between it and the mean.

Question 5

A distribution of playing cards is normally distributed.

Question 6

Extreme scores on the normal curve are those far from the mean.

Question 7

The numerator of the z score in Chapter 7 is a standard deviation.

Question 8

A z score of -1.05 is possible.

Question 9

The total area of each theoretical distribution described in Chapter 7 was 1.00.

Question 10

Equal distances on the X axis are associated with equal proportions of the normal curve.

Question 11

If an urn contains 2 red balls, 2 blue balls, and 1 green ball, the probability of drawing a blue ball is .20.

Question 12

Theoretical distributions are based on mathematics and logic.

Question 13

The inflection points on the normal curve are at one standard deviation above the mean and one standard deviation below the mean.

Question 14

A point on the normal curve with .15 of the curve below it has .35 between it and the mean.

Question 15

A rectangular distribution is an example of a normal distribution.

Question 16

Extreme scores on the normal curve are those near the mean.

Question 17

The denominator of the z score in Chapter 7 is a standard deviation.

Question 18

The total area of theoretical distributions described in Chapter 7 was 1.00.

Question 19

A z score of -1.05 is not possible.

Question 20

The size of the area of the theoretical distributions described in Chapter 7 depends on the size of the population.

Question 21

If an urn contains 2 red balls, 2 blue balls, and 1 green ball, the probability of drawing a green ball is .10.

Question 22

Empirical distributions are not based on mathematics or logic.

Question 23

The inflection points on the normal curve are at the mean and the median.

Question 24

A point on the normal curve with .40 of the curve beyond it has .10 between it and the mean.

Question 25

The normal distribution is symmetrical about the median.

Question 26

Extreme scores on the normal curve are those between the mean and the median.

Question 27

The numerator of the z score in Chapter 7 is the difference between a distribution's mean and its median.

Question 28

The area of a portion of a theoretical distribution is always equal to the probability of the events covered by that area.

Question 29

Your textbook used positive and negative z scores as measures along the X axis.

Question 30

The size of the theoretical distributions described in Chapter 7 does not depend on the size of the population.

Question 31

Data Set 7-1: Suppose an urn (a kind of jar that seems to be the best natural habitat for marbles) contained 3 red, 6 black, 5 blue, 2 yellow and 4 green marbles.

-Refer to Data Set 7-1. The probability of drawing a blue marble is

A) .20
B) .25
C) 5
D) none of the other alternatives are correct.

Question 32

Data Set 7-1: Suppose an urn (a kind of jar that seems to be the best natural habitat for marbles) contained 3 red, 6 black, 5 blue, 2 yellow and 4 green marbles.

-Refer to Data Set 7-1. The probability of drawing a black or a green marble is

A) .06
B) .40
C) .60
D) none of the other alternatives are correct

Question 33

Data Set 7-1: Suppose an urn (a kind of jar that seems to be the best natural habitat for marbles) contained 3 red, 6 black, 5 blue, 2 yellow and 4 green marbles.

-Refer to Data Set 7-1. The probability of drawing a marble that is red, yellow, black or green is

A) .25
B) .50
C) .75
D) 1.00.

Question 34

Data Set 7-2: In the Fall of 1902 there were 184 seniors, 179 juniors, 267 sophomores, and 353 freshmen enrolled at a small college.

-In Data Set 7-2 the probability of picking a student at random and getting a freshman is

A) .353
B) .359
C) .250
D) none of the other alternatives are correct.

Question 35

Data Set 7-2: In the Fall of 1902 there were 184 seniors, 179 juniors, 267 sophomores, and 353 freshmen enrolled at a small college.

-In Data Set 7-2 the probability of picking a student at random and getting either a junior or a senior is

A) .363
B) .184
C) .369
D) none of the other alternatives are correct.

Question 36

Data Set 7-2: In the Fall of 1902 there were 184 seniors, 179 juniors, 267 sophomores, and 353 freshmen enrolled at a small college.

-Data Set 7-2 is

A) a theoretical distribution
B) a normal distribution
C) an empirical distribution
D) none of the other alternatives are correct.

Question 37

Data Set 7-3: A population of scores was normally distributed with a mean of 32 and a standard deviation of 3.

-Look at Data Set 7-3. The proportion that scored between 30 and 27 is

A) .2989
B) .2039
C) .7011

Question 38

Data Set 7-3: A population of scores was normally distributed with a mean of 32 and a standard deviation of 3.

-For Data Set 7-3, the scores that separate the middle 60 percent from the extremes are

A) 28.16, 35.84
B) 29.48, 34.52
C) 30.35, 33.56
D) none of the other alternatives are correct.

Question 39

Data Set 7-3: A population of scores was normally distributed with a mean of 32 and a standard deviation of 3.

-Look at Data Set 7-3. The proportion of the distribution with scores of 30 or more is

A) .7486
B) .6700
C) .2486
D) none of the other alternatives are correct.

Question 40

Data Set 7-4: A set of scores with a mean of 16 and a standard deviation of 3.

-Look at Data Set 7-4. What score separates the top 30 percent of the population from the lower 70 percent?

A) 17.80
B) 18.52
C) 17.00
D) none of the other alternatives are correct.

Question 41

Data Set 7-4: A set of scores with a mean of 16 and a standard deviation of 3.

-Look at Data Set 7-4. What scores are so extreme they are made by only five percent of the population?

A) 11.00, 20.00
B) 11.18, 20.82
C) 10.12 21.88
D) none of the other alternatives are correct.

Question 42

Data Set 7-4: A set of scores with a mean of 16 and a standard deviation of 3.

-Look at Data Set 7-4. What proportion of the population has scores between 12 and 17, including both 12 and 17?

A) .2789
B) .4962
C) .5375
D) none of the other alternatives are correct.

Question 43

Data Set 7-4: A set of scores with a mean of 16 and a standard deviation of 3.

-Look at Data Set 7-4. Suppose 200 persons received scores during a period of a week. How many would have scores of 15 or larger?

A) 15
B) 100
C) 45
D) none of the other alternatives are correct.

Question 44

Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.

-Look at Data Set 7-5. To use Table C in the back of your text, you must assume that

A) the population was a theoretical one
B) the population was normally distributed
C) the highest score possible is 300
D) all of the other alternatives are correct.

Question 45

Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.

-Use Table C to answer questions about Data Set 7-5. The proportion of the population with scores less than 225 is

A) .9332
B) .4332
C) .05668

Question 46

Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.

-Use Table C and Data Set 7-5. The proportion of the population with scores less than 0 is

A) .0000
B) .9987
C) .4987
D) .0013

Question 47

Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.

-If Data Set 7-5 were based on 500 scores, the number with scores between 175 and 200 would be

A) 266
B) 225
C) 75
D) 106

Question 48

Data Set 7-5: Suppose you knew that a population had a mean of 150 and a standard deviation of 50.

-The proportion of the population of scores in Data Set 7-5 that is between 100 and 175 would be

A) .3413
B) .1915
C) .1498
D) .4706

Question 49

Data Set 7-6, a theoretical distribution:

-Look at Data Set 7-6. The probability of occurrence of Event B or Event E is

A) 1.00
B) .25
C) .35
D) .45.

Question 50

Data Set 7-6, a theoretical distribution:

-Look at Data Set 7-6. This distribution is

A) empirical and skewed
B) empirical and rectangular
C) theoretical and skewed
D) theoretical and rectangular.

Question 51

Data Set 7-6, a theoretical distribution:

-Look at Data Set 7-6. The probability of occurrence of Events B or C is

A) 1.00
B) 0.45
C) 0.05
D) 0.80

Question 52

The difference between an empirical distribution and a theoretical distribution is that a theoretical distribution

A) is based on many more observations
B) is theory and cannot be used
C) is based on mathematics and logic
D) is based solely on observation.

Question 53

A characteristic that always distinguishes an empirical from a theoretical curve is

A) the smoothness of the curve or line that connects the points
B) how the points on the curve were obtained
C) whether the curve actually crosses the X axis or not
D) all of the other alternatives are correct.

Question 54

An empirical distribution is based on

A) observations
B) logic
C) both observation and logic
D) neither observation nor logic.

Question 55

An empirical distribution is based on

A) observation
B) logic
C) mathematical formulas
D) all of the other alternatives are correct.

Question 56

Which of the following is a theoretical distribution?

A) a bar graph of the distribution of votes for the five candidates in the last governor's election
B) a bar graph of the number of people in three racial categories in Sam Houston Elementary School in Austin, Texas
C) a frequency polygon of the ages of all students in SHES four years from now
D) a frequency polygon of the number of speaking engagements during the month of October by the winning candidate in last November's election.

Question 57

Which of the following is a theoretical distribution?

A) a count of the number of cups of coffee consumed during each hour of the day
B) a count of the number of cups of coffee consumed during each day of the week
C) a count of the number of cups of coffee consumed during each month of the year
D) none of the other alternatives are correct.

Question 58

Which of the following is a theoretical distribution?

A) your statistics professor stayed in the residence hall one Friday night and flipped a coin 10,000 times. The number of heads and tails was recorded.
B) The price of every house sold in the last five years in Hampden County was obtained from courthouse records.
C) The number of persons who arrived late was recorded every time a statistics course met during the semester.
D) None of the other alternatives are correct.

Question 59

Which of the following is an empirical distribution?

A) the given names and their frequencies of all high school graduates in the United States for the year 2010
B) the scores obtained from an infinite number of throws of one die
C) the normal distribution contained in Table C in your text
D) all of the other alternatives are correct.

Question 60

Suppose that should k occur, it will be called a success. If j should occur, it will be called a failure. The ratio of k/(k + j) is

A) the empirical probability of k
B) the empirical probability of j
C) the theoretical probability of k
D) the theoretical probability of j.

Question 61

Suppose that should k occur, it will be called a success. If j should occur, it will be called a failure. The ratio of k/(k + j) is

A) the theoretical probability of k
B) the empirical probability of k
C) both of the descriptive alternatives
D) neither of the descriptive alternatives.

Question 62

Suppose that should k occur, it will be called a success. If j should occur, it will be called a failure. The ratio of k/(k + j) is

A) the empirical probability of k
B) the empirical probability of j
C) both of the descriptive alternatives
D) neither of the descriptive alternatives.

Question 63

Suppose that if k should occur, it will be called a success. If j should occur, it will be called a failure. The ratio $\frac { k } { j }$ is

A) the empirical probability of k
B) the empirical probability of j
C) the theoretical probability of k
D) none of the other alternatives are correct.

Question 64

Suppose that if k should occur, it will be called a success. If j should occur, it will be called a failure. The ratio k/(k+j) is

A) the empirical probability of k
B) the empirical probability of j
C) the theoretical probability of k
D) the theoretical probability of j.

Question 65

You would know the probability of an event or events if you knew

A) the number of successes that occurred
B) the total number of events
C) the proportion of the curve that corresponded to the event(s)
D) none of the other alternatives are correct.

Question 66

Suppose you had 5 coins which you tossed in the air 100 times and recorded the number of heads on each toss. The distribution you generated would be a one.

A) rectangular
B) binomial
C) normal.

Question 67

Five coins are tossed 100 times. The distribution generated is

A) theoretical
B) empirical.

Question 68

A distribution that is not a normal distribution is

A) abnormal
B) not useful
C) the result of faulty observations
D) none of the other alternatives are correct.

Question 69

Which of the following is a normal distribution?

A) number choices between one and ten
B) playing cards drawn from a deck
C) both of the descriptive alternatives
D) neither of the descriptive alternatives.

Question 70

When a theoretical distribution is used to assess probability, the area under the curve is considered to be

A) 0.00
B) 1.00
C) 2.00
D) any of the other alternatives are possible.

Question 71

The total area under a theoretical distribution is

A) 1.00
B) dependent upon the number of events
C) dependent upon the mean
D) dependent upon the mean, standard deviation, and number of events.

Question 72

The area under part of a theoretical curve is also

A) the mean of the curve
B) the standard deviation of the curve
C) the probability of events covered by that area of the curve.

Question 73

Rectangular, binomial and normal curves have the following in common:

A) The most frequent score is in the middle of the distribution
B) Table C gives the probabilities for all three curves
C) The area under the curve is 1.00
D) All of the other alternatives are correct.

Question 74

For distributions that are not normal distributions

A) Table C cannot be used
B) probabilities cannot be calculated
C) empirical observations cannot fit a theoretical distribution
D) all of the other alternatives are correct.

Question 75

To use the theoretical normal curve, which of the following things must be known about the population?

A) mean
B) standard deviation
C) the form of the distribution
D) all of the other alternatives are correct.

Question 76

The mean and standard deviation of standard intelligence tests is

A) 0, 1.00
B) 100, 1.00
C) 100, 15
D) 1.00, 0.00.

Question 77

According to your text the following data are distributed normally.

A) truck driver wages
B) pine tree diameters
C) both truck driver wages and pine tree diameters
D) neither truck driver wages nor pine tree diameters.

Question 78

Please do not use your table in answering this question. .3849 of the normal curve falls between $\mu$ and 1.2 $\sigma$ . The proportion between $\mu$ and .6 $\sigma$ is

A) .7698
B) .19245
C) .69245
D) not determinable from the information given.

Question 79

.4332 of the normal curve lies between $\mu$ and 1.5 $\sigma$ . The proportion between $\mu$ and .75 $\sigma$ is

A) .8664
B) .2166
C) .0668
D) not determinable without a table of the normal curve.

Question 80

.2580 of the normal curve lies between $\mu$ and .70 $\sigma$ . The proportion between $\mu$ and .35 $\sigma$ is

A) .1240
B) .1290
C) .5160
D) not determinable unless the normal curve table is consulted.