Deck 6: The Normal Distribution

Question 1

If behavior problem scores are roughly normally distributed in the population, a sample of behavior problem scores will

A) be normally distributed with any size sample.
B) more closely resemble a normal distribution as the sample size increases.
C) have a mean of 0 and a standard deviation of 1.
D) be negatively skewed.

Answer 1

more closely resemble a normal distribution as the sample size increases.

Question 2

The normal distribution is

A) most frequently observed for the distribution of small sample sizes.
B) characterized by a high degree of skewness.
C) a distribution with a known shape and other properties.
D) the distribution that we would expect for the salaries of basketball players.

Answer 2

a distribution with a known shape and other properties.

Question 3

We care a great deal about areas under the normal distribution because

A) they translate directly to expected proportions.
B) they are additive.
C) they allow us to calculate probabilities of categories of outcomes.
D) all of the above

Answer 3

all of the above

Question 4

If a population of behavior problem scores is reasonably approximated by a normal distribution, we would expect that the X axis would

A) have values between 0 and 4.
B) have values between -1 and +1.
C) have only negative values.
D) We cannot say what the values on that axis would be.

Question 5

There are a few z scores that we use often that are worth remembering. The upper 50%, and 97.5 percent of a normal distribution are cut off by z scores of

A) 1.0, and 1.64.
B) 0.0, and 1.96.
C) .50, and .975.
D) plus and minus 1.96.

Question 6

We know that 25% of the class got an A on the last exam, and 30% got a B. What percent got either an A or a B?

A) 25% × 30% = 7.5%
B) 25% + 30 % = 55%
C) 45%
D) We cannot tell from the information that is presented.

Question 7

The tables of the standard normal distribution contain only positive values of z . This is because

A) the distribution is symmetric.
B) z can take on only positive values.
C) we aren't interested in negative values of z .
D) probabilities can never be negative.

Question 8

A linear transformation of data

A) multiplies all scores by a constant and/or adds some constant to all scores.
B) is illegal.
C) drastically changes the shape of a distribution.
D) causes the data to form a straight line.

Question 9

If we know that the probability for z > 1.5 is .067, then we can say that

A) the probability of exceeding the mean by more than 1.5 standard deviations is .067.
B) the probability of being more than 1.5 standard deviations away from the mean is .134.
C) 86.6% of the scores are less than 1.5 standard deviations from the mean.
D) all of the above

Question 10

The ordinate of a normal distribution is often labeled

A) frequency.
B) X.
C) density.
D) proportion.

Question 11

Which of the following is a good reason to convert data to z scores?

A) We want to be able to estimate probabilities or proportions easily.
B) We think that it is easier for people to work with round numbers.
C) We want to make a skewed set of data into a normally distributed set of data.
D) all of the above

Question 12

The symbol p is commonly used to refer to

A) any value for the observed variable.
B) a value from a standard normal distribution.
C) the probability for the occurrence of an observation.
D) none of the above

Question 13

If you are interested in identifying children who are highly aggressive, and you have a normally distributed scale that will do so, you will be particularly interested in

A) scores on that scale that are substantially above the mean.
B) scores on that scale that are substantially far from the mean.
C) scores on that scale that are substantially below the mean.
D) any extreme score.

Question 14

Knowing that data are normally distributed allows me to

A) calculate the probability of obtaining a score greater than some specified value.
B) calculate the probability of obtaining a score of exactly 1.
C) calculate what range of values are unlikely to occur by chance.
D) both a and c

Question 15

The distribution that is normally distributed with a mean of 0 and a standard deviation of 1 is called

A) the normal distribution.
B) the standard normal distribution.
C) the skewed normal distribution.
D) the ideal normal distribution.

Question 16

If behavior problem scores are normally distributed, and we want to say something meaningful about what values are likely and what are unlikely, we would have to know

A) the mean.
B) the standard deviation.
C) the sample size.
D) both a and b

Question 17

The formula for calculating the 95% probable limits on an observation is

A) (µ > 1.96 s )
B) ( s + 1.96µ)
C) (µ - 1.96 s )
D) (µ ± 1.96 s )

Question 18

A z score of 1.25 represents an observation that is

A) 1.25 standard deviation below the mean.
B) 0.25 standard deviations above the mean of 1.
C) 1.25 standard deviations above the mean.
D) both b and c

Question 19

The difference between the histogram of 175 behavior problem scores and a normal distribution is

A) the normal distribution is continuous, while behavior problem scores are discrete.
B) the normal distribution is symmetric, while behavior problem scores may not be.
C) the ordinate of the normal distribution is density, the ordinate for behavior problems is frequency.
D) Each of the previous choices is correct.

Question 20

The text discussed setting "probable limits" on an observation. These limits are those which have a

A) 50% chance of enclosing the value that the observation will have.
B) 75% chance of enclosing the value that the observation will have.
C) 80% chance of enclosing the value that the observation will have.
D) 95% chance of enclosing the value that the observation will have.

Question 21

The difference between a normal distribution and a standard normal distribution is

A) standard normal distributions are more symmetric.
B) normal distributions are based on fewer scores.
C) standard normal distributions always have a mean of 0 and a standard deviation of 1.
D) there is no difference.

Question 22

The difference between a standard score of -1.0 and a standard score of 1.0 is

A) the standard score 1.0 is farther from the mean than -1.0.
B) the standard score -1.0 is farther from the mean than 1.0.
C) the standard score 1.0 is above the mean while -1.0 is below the mean.
D) the standard score -1.0 is above the mean while 1.0 is below the mean.

Question 23

If the test scores on an art history exam were normally distributed with a mean of 76 and standard deviation of 6, we would expect

A) most students scored around 70.
B) no one scored 100 on the exam.
C) almost equal numbers of students scored a 70 and an 82.
D) both a and c

Question 24

Transforming a set of data to a new mean and standard deviation using a linear transformation

A) alters the shape of the distribution.
B) makes the scores harder to work with.
C) is rarely permissible.
D) is something we do frequently.

Question 25

When we transform scores to a distribution that has a mean of 50 and a standard deviation of 10, those scores are called

A) z scores.
B) t scores.
C) T scores.
D) stanine scores.

Question 26

Assume that your class took an exam last week and the mean and standard deviation of the exam were 85 and 5, respectively. Your instructor told you that 30 percent of the students had a score of 90 or above. You would probably

A) think that your instructor was out of her mind.
B) decide that your score of 80 would probably fall in the failing range.
C) conclude that the scores were not normally distributed.
D) conclude that such a set of scores could not possibly happen.

Question 27

The normal distribution is often referred to as the bell curve.

Question 28

In a normal distribution, about how much of the distribution lies within two (2) standard deviations of the mean?

A) 33% of the distribution
B) 50% of the distribution
C) 66% of the distribution
D) 95% of the distribution

Question 29

The most common situation in statistical procedures is to assume that

A) data are positively skewed.
B) data are negatively skewed.
C) data are normally distributed.
D) it doesn't make any difference what the distribution of the data looks like.

Question 30

Stanine scores

A) are badly skewed.
B) have a mean of 5 and vary between 1 and 9.
C) are always integers.
D) both b and c

Question 31

If we have data that have been sampled from a population that is normally distributed with a mean of 50 and a standard deviation of 10, we would expect that 95% of our observations would lie in the interval that is approximately

A) 30-70.
B) 35-50.
C) 45-55.
D) 70-90.

Question 32

Which of the following is NOT always true of a normal distribution?

A) It is symmetric.
B) It has a mean of 0.
C) It is unimodal.
D) both a and b

Question 33

We are interested in what the text calls "probable limits" because

A) we want to know whether a piece of data is unusual.
B) we want to have a good idea what kinds of values to expect.
C) we might want to know whether values below some specific value are improbable.
D) all of the above

Question 34

"Abscissa" is to _______ as "ordinate" is to _______.

A) density; frequency
B) frequency; density
C) horizontal; vertical
D) vertical; horizontal

Question 35

An example of a linear transformation is

A) converting heights from feet to meters.
B) subtracting the value of the mean from each individual IQ score and dividing by the value of the standard deviation.
C) both a and b
D) none of the above

Question 36

For a normal distribution

A) all of the data points lie within one standard deviation from the mean.
B) about 2/3 of the distribution lies within one standard deviation from the mean.
C) about 95% of the distribution lies within two standard deviations from the mean.
D) both b and c

Question 37

The difference between "probable limits" and "confidence limits" is that the probable limits

A) focus on estimating where a particular score is likely to lie using a known population mean.
B) estimate the kinds of means that we expect.
C) try to set limits that have a .95 probability of containing the population mean.
D) There is no difference.

Question 38

The advantage of using T-scores and standard scores is

A) those scores provide a common form of reference to everyone using them.
B) only negative numbers are used.
C) the mean is always 10.
D) scores of -1 and +1 are equal distances from the mean.

Question 39

A normal distribution

A) has more than half of its data points to the left of the median.
B) has more than half of its data points to the right of the mean.
C) has 95% of its data points within one standard deviation of the mean.
D) is symmetrical.

Question 40

A test score of 84 was transformed into a standard score of -1.5. If the standard deviation of test scores was 4, what is the mean of the test scores?

A) 78
B) 80
C) 90
D) 88

Question 41

Using the distribution in the previous question, calculate z scores for:
a. X = 11
b. X = 35
c. X = 71

Question 42

Most statistical techniques are based on the assumption that the population of observations is not normal.

Question 43

Create a z distribution based on the following data. Explain the process.
10 20 20 30 30 30 40 40 40 40 50 50 50 60 60 70

Question 44

A z score refers to the number of standard deviations above or below the mode.

Question 45

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Question 46

The normal distribution is bimodal and symmetric.

Question 47

The basketball team lives in another dorm from those in the previous question. Their heights are normally distributed as well, with a mean height of 71 inches and a standard deviation of 2 inches.
a. Draw their distribution on the same graph as students who lived in the first dorm (e.g., draw separate but overlapping distributions).
b. What percent of students in the first dorm are at least as tall as the average basketball players?
c. What percent of basketball players are taller than the average dorm resident?

Question 48

Based on the previous data, we could conclude that 90% of the students are likely to fall between what heights?

Question 49

Based on the height data in the previous question:
a. What percent of residents are between 65 inches and 71 inches tall?
b. What percent of residents are taller than 72 inches?
c. What percent of residents are shorter than 72 inches?

Question 50

The area under a particular portion of the normal curve is equivalent to theprobability of falling within that portion of the distribution.

Question 51

The probability that a student will score between plus or minus one standard deviation from the mean on an exam, assuming the scores are normally distributed, is approximately 68%.

Question 52

The birth weight of healthy, full term infants in the United States is nearly normally distributed. The mean weight is 3,500 grams, and the standard deviation is 500 grams.
 
a. What percent of healthy newborns will weigh more than 3,250 grams?
b. What weights would 95% of all healthy newborns tend to fall between?
c. What is the z score for an infant who weighs 2,750 grams?
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Question 53

In a normal distribution, indicate what percent of scores fall:
a. between the mean and 1 standard deviation above the mean
b. between plus and minus 2 standard deviations of the mean.
c. 3 standard deviations above or below the mean.

Question 54

In a normal distribution, the majority of scores fall beyond plus or minus one standard deviation from the mean.

Question 55

At a neighboring university, the average salary is also $45,000 and the distribution is normal. If $47,000 has a z score of 1.5, what is the standard deviation?

Question 56

If the salary of assistant professors in this university is normally distributed with a mean of $45,000 and a standard deviation of $1,500, what salary would have a z score of .97?

Question 57

The height of students in a dormitory is normally distributed with a mean of 68 inches and a standard deviation of 3 inches. Draw the distribution.

Question 58

Performing a linear transformation can make any distribution normal.

Question 59

Suzie scored in the 95^th percentile on the Math portion of the SAT. This means that she scored as high or higher than 95% of the other students who took the test.