Deck 6: Where Am I Normal Distributions and Standard Scores

Question 1

An IQ score on the Stanford-Binet test is an unstandardized score.

Answer 1

False

Question 2

A deviation score is the numerator of the formula for calculating a z-score.

Answer 2

True

Question 3

A deviation score is obtained by subtracting the observed mean from the population mean.

Answer 3

False

Question 4

A deviation score in the z-score formula cannot be replaced by the mode of the sample.

Question 5

Someone's z-score on a test can only be known if we know both the population mean of the test and the standard deviation.

Question 6

An individual who scores higher than the mean on a test will have a z-score that is negative.

Question 7

Jessica scores the same as the mean on a test. Her z-score is zero.

Question 8

The closer the score is to the mean, the less frequent it is in the distribution.

Question 9

The 3-sigma rule describes the distribution of observations in a skewed distribution.

Question 10

A test of spatial skill has a mean of 200 and a standard deviation of 10. A newer, different test of spatial skills has a mean of 50 and a standard deviation of 15. A score of 100 would be more common in the new test than in the older test.

Question 11

Under the 3-sigma rule, 98% of observations will be within two standard deviations from the mean.

Question 12

The 3-sigma rule is violated when the mean, mode and median are the same value.

Question 13

To find out the probability of obtaining any given score on a test as compared to the population, you will need at least the mean and standard deviation.

Question 14

In a normal distribution of scores from a test, the median is the score that occurs the most often.

Question 15

In a symmetric distribution, the probability of obtaining a z-score above 3 is exactly the same as the probability of obtaining a z-score below -3.

Question 16

If you obtain an observed z-score that is larger than critical z, you should always reject the null hypothesis.

Question 17

Dean would like to compare the relative performance of his son, Andy, on two different tests of verbal fluency. Even though he has Andy's scores, and the typical score and standard deviation for both tests, Dean has insufficient information.

Question 18

To standardize scores, we only need to know the shape of the distribution and the standard deviation.

Question 19

To use the z-test, you need to know only one population parameter.

Question 20

The z-test is a popular test because it is easy to calculate and does not make assumptions about the distribution of the data.

Question 21

Which of the following information is missing from non-standard scores that is present in standard scores?

A) The range of scores from the lowest to highest.
B) The actual value of a measurement in nature, accounting for error.
C) The change in an individual's scores over time.
D) The location of individual scores in a set, relative to the mean

Question 22

The difference in height between the tallest and shortest student in a class is a:

A) Standard score
B) Standard deviation
C) Range
D) Z-score

Question 23

Jaime and Gina are comparing SAT scores. The scores are standardized and range from 200 to 800 for each section. Jaime scored 750 on the verbal section, while Gina scored 760 in the same section. Which of the following statements is true?

A) Since the scores are standardized, neither Jaime's nor Gina's score will change even if they took the test again.
B) Jaime's score is a lower percentile than Gina's score.
C) Jaime answered 10 fewer questions correctly on the test than Gina did.
D) Since they do not know the scores of every individual who has taken the test, both Gina and Jaime will not be able to find out how their scores rank against everyone else.

Question 24

Suzanne would like to calculate the z-score of her height relative to the height of ballerinas. She is 5'7. What other information does she need to obtain the z-score of her height?

A) Mean height of all ballerinas in general, and the standard deviation
B) Mean height of ballerinas in her class, and the standard error
C) The most common height of ballerinas, and the standard deviation
D) The most common height of ballerinas, and the range

Question 25

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ Carissa is working to conserve the last surviving mutant cats. The table above displays the distribution of weight of the last existing population of mutant cats. Which of the following is the best description of the mean, mode and median of mutant cat weight?

A) The mode and median are the same.
B) The mean is lower than the mode.
C) The mode is lower than the median.
D) The median is lower than the mean and the mode.

Question 26

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ Which of the following is true about the weight of mutant cats?

A) The weight of mutant cats is normally distributed.
B) The weight of mutant cats is positively skewed.
C) The weight of mutant cats is negatively skewed.
D) The weight of mutant cats is a continuous uniform distribution.

Question 27

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ What is the standard deviation?

A) 9.06
B) 1.56
C) 3.32
D) 9.0

Question 28

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ A mutant cat that weighs 8 pounds has a deviation score of:

A) 1
B) 0
C) -1
D) -4

Question 29

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ If a mutant cat weighs 11 pounds, its weight converts to a z-score of:

A) 2.0
B) 1.5
C) 1.3
D) 1.2

Question 30

$$\begin{array} { | c | c | } \hline \text { Weight (pounds) } & \text { Frequency } \\\hline 6 & 1 \\\hline 7 & 2 \\\hline 8 & 2 \\\hline 9 & 5 \\\hline 10 & 3 \\\hline 11 & 2 \\\hline 12 & 1 \\\hline\end{array}$$ A mutant cat that lives in a zoo in Germany has a weight z-score of zero. Its weight in pounds is closet to:

A) 6
B) 8
C) 9
D) 10

Question 31

Given that Jack's score on a test with a mean of 10 and standard deviation of 2 is 15, what is his z-score on the test?

A) -2.5
B) 2.5
C) -3
D) 3

Question 32

Margo's z-score on a test is 0.6; her actual score is 50 and the mean of the test is 51. What is the standard deviation of the test?

A) -1.67
B) 1.67
C) -1.63
D) 1.63

Question 33

Josh's z-score on a test is -0.5. Which of the following options must be true?

A) Josh scored better than 65% of other test takers.
B) Josh scored better than 25% of other test takers.
C) Josh scored worse than 16% of other test takers.
D) Josh scored worse than 72% of other test takers.

Question 34

A test of spatial skills has a mean of 80 and a standard deviation of 5. A newer, different test that also measures spatial skills has a mean of 100 and a standard deviation of 2. The distribution of the older test is ________________ than the distribution of the newer test.

A) narrower
B) the same
C) wider
D) more skewed

Question 35

A test of spatial skills has a mean of 70 and a standard deviation of 6. A different test for vocabulary knowledge has the same mean and standard deviation. Which of the following options is true?

A) A z-score of -2 on the test of spatial skills is the same distance from the mean as a raw score of 120 on the test for vocabulary knowledge.
B) A z-score of -1.5 on the test of spatial skills is the same distance from the mean as a raw score of 85 on the test for vocabulary knowledge.
C) A raw score of 135 on the test of spatial skills is not the same distance from the mean as a z-score of 3.5 on the test for vocabulary knowledge.
D) A raw score of 90 on the test of spatial skills is the same distance from the mean as a z-score of 1.

Question 36

Under the 3-sigma rule, 96% of observations would be within how many standard deviations from the mean?

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

Question 37

Given that Sophie's deviation score on a test is -0.05 and the standard deviation of the test is 1.4, what is her z-score?

A) -0.036
B) 0.035
C) -0.07
D) 0.07

Question 38

What is the difference in probability of getting a z-score of at least 0 and getting a z-score of at least 0.5?

A) 0
B) .1915
C) .5000
D) .8413

Question 39

Brittney's z-score is 0 on a test with a mean of 100 and a standard deviation of 10. Jessica's z-score is 0.33 on the same test. What is the difference between their raw scores?

A) 103.3
B) 3.3
C) 13.3
D) 0.33

Question 40

Last semester, Julia scored 140 on an intelligence test with a mean of 100 and standard deviation of 10. This year, she scored 100 on a different intelligence test with a mean of 60 and standard deviation of 10. Which of the following statements is true in relation to Julia's scores?

A) Julia performed better this year.
B) Julia performed better last year.
C) Julia performed equally well in both years.
D) None of the above.

Question 41

$$\begin{array} { | l | l | } \hline \text { Length (inch) } & \text { Frequency } \\\hline 0.1 & 2 \\\hline 0.2 & 3 \\\hline 0.3 & 3 \\\hline 0.4 & 5 \\\hline 0.5 & 4 \\\hline 0.6 & 2 \\\hline 0.7 & 2 \\\hline\end{array}$$ Adele is studying a new species of insect that emits an odor perceived to be pleasant to humans. The known population consists of 21 insects. Adele has measured the length of each one.
What is the population mean?

A) 0.3
B) 0.4
C) 0.5
D) 0.6

Question 42

$$\begin{array} { | l | l | } \hline \text { Length (inch) } & \text { Frequency } \\\hline 0.1 & 2 \\\hline 0.2 & 3 \\\hline 0.3 & 3 \\\hline 0.4 & 5 \\\hline 0.5 & 4 \\\hline 0.6 & 2 \\\hline 0.7 & 2 \\\hline\end{array}$$ Adele is studying a new species of insect that emits an odor perceived to be pleasant to humans. The known population consists of 21 insects. Adele has measured the length of each one.
An insect that is 0.7 inches long would have a deviation score of:

A) 0
B) 0.1
C) 0.2
D) 0.3

Question 43

$$\begin{array} { | l | l | } \hline \text { Length (inch) } & \text { Frequency } \\\hline 0.1 & 2 \\\hline 0.2 & 3 \\\hline 0.3 & 3 \\\hline 0.4 & 5 \\\hline 0.5 & 4 \\\hline 0.6 & 2 \\\hline 0.7 & 2 \\\hline\end{array}$$ Adele is studying a new species of insect that emits an odor perceived to be pleasant to humans. The known population consists of 21 insects. Adele has measured the length of each one.
An insect that is 0.2 inches long would have a deviation score of:

A) 0
B) -0.1
C) 0.1
D) -0.2
E) 0.2

Question 44

$$\begin{array} { | l | l | } \hline \text { Length (inch) } & \text { Frequency } \\\hline 0.1 & 2 \\\hline 0.2 & 3 \\\hline 0.3 & 3 \\\hline 0.4 & 5 \\\hline 0.5 & 4 \\\hline 0.6 & 2 \\\hline 0.7 & 2 \\\hline\end{array}$$ Adele is studying a new species of insect that emits an odor perceived to be pleasant to humans. The known population consists of 21 insects. Adele has measured the length of each one.
Adele discovers a new specimen of this insect species. It is 0.5 inches long. What is its z-score?

A) 0.50
B) 0.61
C) 0.71
D) 0.80

Question 45

$$\begin{array} { | l | l | } \hline \text { Length (inch) } & \text { Frequency } \\\hline 0.1 & 2 \\\hline 0.2 & 3 \\\hline 0.3 & 3 \\\hline 0.4 & 5 \\\hline 0.5 & 4 \\\hline 0.6 & 2 \\\hline 0.7 & 2 \\\hline\end{array}$$ Adele is studying a new species of insect that emits an odor perceived to be pleasant to humans. The known population consists of 21 insects. Adele has measured the length of each one.
An insect in the original population is shorter than 96% of the class. How long is this particular insect?

A) 0.1
B) 0.2
C) -0.2
D) -0

Question 46

What is the difference in probability of getting a z-score of at least 0.3 and getting a z-score of at least 1.75? Show each step of your calculation.

Question 47

Natalie had a score of 55 on a test with a mean of 40 and standard deviation of 8. What is her percentile rank on the test, to the nearest percent?

Question 48

Lucia hypothesizes that her friends scored better than the average student on a physics exam. She obtains the exam scores of her 4 friends and calculates the average score, which is 86%. If the overall average for the exam is 82% with a standard deviation of 3.2, is Lucia's hypothesis supported, assuming an alpha level of 0.05? Why?

Question 49

Kristie's z-score is -2.01 on a test with a mean of 70 and standard deviation of 2. What is her raw score? Round your answer to the nearest whole number.

Question 50

Lewis obtained a score of 45 on a test with a mean of 55 and a standard deviation of 10. What is the percentile of Lewis' score? Round your answer to the nearest whole number.