Question 1

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

Accepted Answer

Non-standard scores do not provide information about the location of individual scores relative to the mean, which is a key component of standard scores such as z-scores. Non-standard scores may provide information on the range of scores, the actual value of measurements, or changes in scores over time, but these do not distinguish them from standard scores.

Question 2

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

Accepted Answer

The difference in height between the tallest and shortest student in a class is a range. Range is a measure of dispersion that gives the difference between the smallest and largest values in a dataset. Standard score, standard deviation, and z-score are all measures of variability, but they do not specifically measure the difference between the tallest and shortest values.

Question 3

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?

Accepted Answer

Since the scores are standardized, the scores will not change if they took the test again (eliminating option A). Since Jaime scored lower than Gina, it means that her score is at a lower percentile (choosing option B). There is not enough information to determine how many questions each got right or how their scores rank against everyone else (eliminating options C and D).

Question 4

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?

Accepted Answer

To calculate the z-score, Suzanne will need the mean and standard deviation of the population (in this case, all ballerinas).

Question 5

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

Accepted Answer

The mode is the most frequently occurring value, which is 9. The median is the middle value when the data is arranged in order, which is also 9. Therefore, the mode and median are the same.

Question 6

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

Accepted Answer

The answer of \[\begin{array} { | c | c |...

Question 7

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

Accepted Answer

The standard deviation is calculated by finding the square root of the variance. The variance is the average of the squared differences from the mean. Here, the mean is 9, and the variance is approximately 2.44, so the standard deviation is about 1.56.

Question 8

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

Accepted Answer

The mean weight of the cats is $$
\frac{6+7	imes2+8	imes2+9	imes5+10	imes3+11	imes2+12}{1+2+2+5+3+2+1}=\frac{83}{15}=5\frac{8}{15}
$$
Therefore, the deviation score of a cat weighing 8 pounds is $$
\frac{8-5\frac{8}{15}}{1.57}\approx -1.01
$$
The closest choice to this value is C) -1.

Question 9

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

Accepted Answer

To find the z-score, we need to use the formula:
z = (x - mean)/standard deviation
First, we need to find the mean and standard deviation from the frequency distribution. The mean is:
mean = sum of (weight * frequency)/total frequency
= (6*1 + 7*2 + 8*2 + 9*5 + 10*3 + 11*2 + 12*1)/16
= 9
The standard deviation is:
standard deviation = square root of [(sum of (frequency * (weight - mean)^2))/(total frequency - 1)]
= square root of [(1*(6-9)^2 + 2*(7-9)^2 + 2*(8-9)^2 + 5*(9-9)^2 + 3*(10-9)^2 + 2*(11-9)^2 + 1*(12-9)^2)/15]
= 1.7889 (rounded to 4 decimal places)
Now we can find the z-score for a weight of 11 pounds:
z = (11 - 9)/1.7889
= 1.1180 (rounded to 4 decimal places)
Therefore, the answer is C) 1.3.

Question 10

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

Accepted Answer

The weight z-score of the mutant cat is 0, which means its weight is at the mean of the distribution. From the table, we see that the weight with the smallest difference from the mean is 9 pounds, with a frequency of 5. Thus, the mutant cat's weight is most likely closest to 9 pounds.

Question 11

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?

Accepted Answer

To find the z-score, we use the formula: 
z = (x - μ) / σ 
where x is the score, μ is the mean, and σ is the standard deviation.

In this case, 
x = 15 
μ = 10 
σ = 2

Plugging these values into the formula, we get: 
z = (15 - 10) / 2 = 2.5

Therefore, the answer is choice B.

Question 12

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?

Accepted Answer

The answer of Margo's z-score on a test is 0.6;...

Question 13

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

Accepted Answer

A z-score of -0.5 indicates that Josh's score is below the mean, but not by a large margin. It typically corresponds to being higher than about 30% of the distribution (though the exact percentage can vary slightly depending on the source). Therefore, the statement that Josh scored better than 25% of other test takers is the most accurate among the given options.

Question 14

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.

Accepted Answer

The standard deviation of the newer test is smaller (2) than the standard deviation of the older test (5), which means that the spread of scores for the newer test is narrower. Therefore, the distribution of the older test is wider (or more spread out) than the distribution of the newer test.

Question 15

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?

Accepted Answer

The answer of A test of spatial skills has a...

Question 16

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

Accepted Answer

According to the 3-sigma rule, 99.73% of observations would be within 3 standard deviations from the mean. Therefore, 96% of observations would be within 2 standard deviations from the mean (i.e. 99.73% - 68.27% = 31.46%, which is divided by 2 to get 15.73% on each side of the mean for a total of 31.46%). Thus, the answer is C) 2.

Question 17

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?

Accepted Answer

The z-score is calculated by dividing the deviation score by the standard deviation. Thus, Sophie's z-score = -0.05 / 1.4 = -0.0357, which rounds to -0.036.

Question 18

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?

Accepted Answer

The probability of getting a z-score of at least 0 is equivalent to the area under the standard normal distribution curve to the right of 0, which is 0.5. The probability of getting a z-score of at least 0.5 is the area under the standard normal distribution curve to the right of 0.5, which is approximately 0.1915. Therefore, the difference in probability is 0.5 - 0.1915 = 0.3085, which is closest to choice B.

Question 19

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?

Accepted Answer

Brittney's raw score is the mean, 100, because her z-score is 0. Jessica's raw score is 0.33 standard deviations above the mean, which is 0.33 * 10 = 3.3 units above 100. Therefore, the difference between their raw scores is 3.3.

Question 20

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?

Accepted Answer

The answer of Last semester, Julia scored 140 on an...

Quiz 6: Where Am I Normal Distributions and Standard Scores