Deck 4: Probability Distributions

Question 1

If you want to determine the likelihood that a particular event will occur, you should calculate the ______.

A) standard deviation
B) z-score
C) probability
D) variance

Answer 1

C

Question 2

If you roll a 6-sided die, what is the probability that it will land on 6?

A) 1/6
B) 2/6
C) 6
D) none of these

Answer 2

A

Question 3

Should your data conform perfectly to a particular distribution?

A) yes; if your data does not conform perfectly, it is not really a distribution
B) yes; all distributions are predictable
C) no; distributions are just prototypes
D) no; real data cannot conform perfectly to a distribution

Answer 3

C

Question 4

If you are drawing from a uniform distribution with scores ranging from 1 to 5, what is the probability of drawing a 4?

A) 1/5
B) 2/5
C) 1
D) none of these

Question 5

What percentage of scores should fall between -1 SD and +1 SD from the mean?

A) 34%
B) 68%
C) 50%
D) none of these

Question 6

If you compute a z-score of 1.5, how many standard deviations is its raw score from the mean?

A) 3 SDs below the mean
B) 1.5 SDs below the mean
C) 1.5 SDs above the mean
D) 3 SDs above the mean

Question 7

If you want to compare scores from one distribution to scores from another distribution, you should ______.

A) compare the directly
B) compare z-scores computed from each
C) compare the means of each distribution
D) compare the square root of each value

Question 8

A business owner is comparing sales between each of his three business locations for the month of July. He finds that sales from Store #3 had a z-score of 2.5. Which of these would accurately describe scores from Store #3?

A) far below the mean
B) slightly below the mean
C) slightly above the mean
D) far above the mean

Question 9

According to your text, while in the midst of solving a statistical calculation, you should carry out all calculations to ______.

A) 1 decimal places
B) 2 decimal places
C) 6 decimal place
D) 10 decimal places

Question 10

If x̄ = 2 and s² = 4, calculate z when x = 4.

A) -2
B) -1
C) 1
D) 2

Question 11

If $\mu$ = 3 and $\sigma$ = 2, calculate z when x = 1.

A) -2
B) -1
C) 1
D) 2

Question 12

If $\mu$ = 3 and $\sigma$ ² = 1, calculate x when z = 0.

A) 0
B) 1
C) 2
D) 3

Question 13

If x̄ = -1 and s² = 4, calculate x when z = 1.

A) 0
B) 1
C) 2
D) 3

Question 14

In a normal distribution, what proportion of scores fall above z = 2?

A) .0091
B) .0107
C) .0197
D) .0228

Question 15

What proportion of scores fall below z = 1.5 in normally distributed data?

A) .0668
B) .9394
C) .0606
D) .9332

Question 16

If x̄ = 2 and s² = 4 and scores are normally distributed, what proportion of scores fall above x = 4?

A) .1587
B) .3085
C) .6915
D) .8413

Question 17

If $\mu$ = 3 and $\sigma$ = 2 and scores are normally distributed, what proportion of scores fall below x = 1?

A) .1587
B) .9192
C) .8413
D) .0808

Question 18

44.04% of scores in a normal distribution fall above what z-score?

A) z = .015
B) z = .010
C) z = .100
D) z = .150

Question 19

74.86% of scores in a normal distribution fall below what z-score?

A) z = -1.44
B) z = -.67
C) z = .67
D) z = 1.44

Question 20

If $\mu$ = 3 and $\sigma$ ² = 1, 2.17% of values are above what raw score?

A) x = 5.02
B) x = 2.02
C) x = 0.98
D) x = 5.17

Question 21

If x̄ = -1 and s² = 4, 18.41% of values are below what raw score?

A) 2.8
B) -1.9
C) -2.8
D) 1.9

Question 22

In normally distributed data, what is the percentile rank of scores at z = 1.7?

A) 43rd
B) 96th
C) 57th
D) 4th

Question 23

What is the percentile rank of scores at z = -2.2 in normally distributed data?

A) 99th
B) 59th
C) 1st
D) 41st

Question 24

If x̄ = 1 and s² = 9 and scores are normally distributed, what is the percentile rank of x = 4?

A) 16th
B) 84th
C) 34th
D) 68th

Question 25

If $\mu$ = 9 and $\sigma$ = 3 and scores are normally distributed, what is the percentile rank of x = 3?

A) 98th
B) 3rd
C) 1st
D) 2nd

Question 26

The 48th percentile is most closely associated with which of the following z-scores?

A) z = -.05
B) z = .32
C) z = .05
D) z = -.32

Question 27

The 80th percentile is most closely associated with which of the following z-scores?

A) z = -.84
B) z = -1.4
C) z = 1.4
D) z = .84

Question 28

Which of the following is an accurate interpretation of z = 2.5?

A) The score is at the 2.5 (3rd) percentile
B) The score is 2.5 standard deviations above the mean
C) 2.5% of scores fall below this z-score
D) 2.5% of scores fall above this z-score

Question 29

Which of the following is an accurate interpretation of the 10th percentile?

A) 10% of scores fall above this point
B) 10% of scores fall below this point
C) 10% of scores are used to calculate this rank
D) 10% of scores are between this point and the mean

Question 30

You would expect that 100% of the data would fall under the curve in a given probability distribution.

Question 31

Constant, normal, and skewed are all types of distributions.

Question 32

When drawing from a uniform distribution, it is equally probable that you will draw any number described by that distribution.

Question 33

A Poisson distribution commonly occurs with small numbers of independent counts.

Question 34

If you convert a distribution of scores to z-scores, the standard deviation of those z-scores will be equal to the standard deviation of the standard normal distribution.

Question 35

The standard normal distribution is also called the z-distribution.

Question 36

If your raw score is greater than the mean, a z-score calculated from that raw score will be a positive number.

Question 37

If z = -2, your raw score is located two standard deviations below the mean.

Question 38

Converting raw scores to z-scores allows you to compare those z-scores across datasets.

Question 39

Regardless of the shape of your original distribution, z-scores computed from that distribution will be normally distributed.

Question 40

The only difference between the z-score formula for samples and the z-score formula for populations is that the z-score formula for populations uses $\mu$ and $\sigma$ instead of x̄ and s.

Question 41

If $\mu$ = 2.5, and $\sigma$ ² = .25, when x = 4, z = 6.

Question 42

If $\begin{array}{l}\mathrm{n} \\x\end{array}$ = 55, and s = 3, when x = 50, z = -2.5.

Question 43

In a distribution where $\mu$ = 3 and $\sigma$ = 2, a z-score of 1.5 is associated with x = 6.

Question 44

The proportion of scores above z = 1.25 is .1056.

Question 45

The proportion of scores below z = .5 is .0000.

Question 46

z = 1.75 is the 4th percentile.

Question 47

z = -2.00 is the 2nd percentile.

Question 48

If x̄ = 8.5, and s = 1, 6.68% of scores are above x = 10.

Question 49

If $\mu$ = 25, and $\sigma$ ² = 4, x = 25 falls at the 25th percentile.

Question 50

List and describe the three types of distributions discussed in Chapter 4. If you were to randomly draw from each of these distributions, what values would you be most likely to draw?

Question 51

Explain how and why you would convert a raw score to a z-score.

Question 52

Imagine you converted a dataset with n = 50 to z-scores. Describe the mean, standard deviation, and shape of the resulting distribution of z-scores.

Question 53

Explain the process by which you convert a z-score to a proportion. How do you know what to look for in the z-table?

Question 54

For the survey variable below, complete the following table.