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

Accepted Answer

Probability is the measure used to determine the likelihood that a particular event will occur.

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

Accepted Answer

A 6-sided die has six faces, each with an equal probability of landing face up. Therefore, the probability of rolling any specific number, including 6, is 1/6.

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

Accepted Answer

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

Accepted Answer

In a uniform distribution with scores ranging from 1 to 5, each score has an equal probability of being drawn. Since there are 5 possible scores, the probability of drawing any specific score, including 4, is 1/5.

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

Accepted Answer

68% of scores fall between -1 SD and +1 SD from the mean because the normal distribution is a bell-shaped curve, and 68% of the area under the curve falls within one standard deviation of the mean.

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

Accepted Answer

A z-score of 1.5 indicates that the raw score is 1.5 standard deviations 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

Accepted Answer

Comparing z-scores computed from each distribution allows for a direct comparison of scores from different distributions, as z-scores represent the number of standard deviations a score is away from the mean within its own distribution.

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

Accepted Answer

A z-score of 2.5 indicates that the sales from Store #3 are far above the mean, as it is 2.5 standard deviations above the average.

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

Accepted Answer

Carrying out calculations to 6 decimal places is a common practice in statistical calculations to ensure precision and minimize rounding errors.

Question 10

If x̄ = 2 and s² = 4, calculate z when x = 4. A) -2 B) -1 C) 1 D) 2

Accepted Answer

z = (x - x̄) / s = (4 - 2) / 2 = 1

Question 11

If $\mu$= 3 and $\sigma$ = 2, calculate z when x = 1.
A) -2
B) -1
C) 1
D) 2

Accepted Answer

The z-score is calculated using the formula z = (x - μ) / σ. Here, μ = 3, σ = 2, and x = 1. So, z = (1 - 3) / 2 = -2 / 2 = -1.

Question 12

If $\mu$= 3 and $\sigma$² = 1, calculate x when z = 0. A) 0 B) 1 C) 2 D) 3

Accepted Answer

The answer of If $\mu$= 3 and $\sigma$² =...

Question 13

If x̄ = -1 and s² = 4, calculate x when z = 1. A) 0 B) 1 C) 2 D) 3

Accepted Answer

The answer of If x̄ = -1 and s² =...

Question 14

In a normal distribution, what proportion of scores fall above z = 2?
A) .0091
B) .0107
C) .0197
D) .0228

Accepted Answer

The answer of In a normal distribution, what proportion of...

Question 15

What proportion of scores fall below z = 1.5 in normally distributed data?
A) .0668
B) .9394
C) .0606
D) .9332

Accepted Answer

In a standard normal distribution, the proportion of scores below a z-score of 1.5 is approximately 0.9332.

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

Accepted Answer

The z-score for x = 4 is (4 - 2) / 2 = 1. The proportion of scores above a z-score of 1 in a standard normal distribution is approximately 0.1587.

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

Accepted Answer

The z-score for x = 1 is calculated as (1 - 3) / 2 = -1.5. Using the standard normal distribution table, the proportion of scores below a z-score of -1.5 is approximately 0.1587.

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

Accepted Answer

The answer of 44.04% of scores in a normal distribution...

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

Accepted Answer

The answer of 74.86% of scores in a normal distribution...

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

Accepted Answer

The z-score corresponding to the top 2.17% of a standard normal distribution is approximately 2. This means the raw score is 2 standard deviations above the mean. Given the mean (μ) is 3 and the standard deviation (σ) is 1, the raw score is 3 + 2(1) = 5.02.

Quiz 4: Probability Distributions

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

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

Should your data conform perfectly to a particular distribution?

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

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

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