Z-Score & Standard Deviation Quiz (HSS.ID.A.4)

1) What is the z-score for an athlete who runs the 100-meter dash in 13.7 seconds?

0.9

-1.5

-0.9

1.5

(13.7 − 12.5) ÷ 0.8 = 1.5

Explanation

(13.7 − 12.5) ÷ 0.8 = 1.5

2) An athlete has a z-score of -1.25 for their 100-meter dash time. What does this indicate?

The athlete’s time is 1.25 seconds slower than average

The athlete’s time is 1.25 standard deviations faster than the mean

The athlete’s time is 1.25 standard deviations slower than the mean

The athlete ran 1.25 seconds faster than average

Negative z means faster than average.

Explanation

Negative z means faster than average.

3) Which raw time corresponds to a z-score of 2.0?

13.3 seconds

14.1 seconds

10.9 seconds

15.7 seconds

12.5 + (2 × 0.8) = 14.1 seconds.

Explanation

12.5 + (2 × 0.8) = 14.1 seconds.

4) If an athlete’s time has a z-score of 0, what can you conclude?

The athlete had the fastest time

The athlete’s time is below average

The athlete’s time equals the mean time

The athlete did not finish the race

z = 0 means same as average.

Explanation

z = 0 means same as average.

5) The formula for calculating a z-score is z = (x − μ) / σ. What does the variable x represent?

The mean of the data set

The standard deviation

The individual data value or raw score

The z-score itself

x is the actual value.

Explanation

x is the actual value.

6) A student scores 85 on a test where the class mean is 78 and the standard deviation is 5. What is the student’s z-score?

0.7

1.4

7.0

-1.4

(85 − 78) ÷ 5 = 1.4

Explanation

(85 − 78) ÷ 5 = 1.4

7) If a data point has a z-score of -2.5, what does this tell you about its position in the distribution?

It is 2.5 units above the mean

It is 2.5 standard deviations below the mean

It is 2.5 standard deviations above the mean

It is exactly at the mean

Negative z = below the mean.

Explanation

Negative z = below the mean.

8) A z-score of 0.5 indicates that a data value is:

Below the mean

Equal to the mean

Above the mean

Equal to the median

Positive z = above average.

Explanation

Positive z = above average.

9) A baby weighs 9.0 pounds at birth. What is this baby’s z-score (rounded to two decimal places)?

1.82

1.64

2.18

0.82

(9.0 − 7.2) ÷ 1.1 = 1.64

Explanation

(9.0 − 7.2) ÷ 1.1 = 1.64

10) Which baby weight would have a negative z-score?

7.2 pounds

8.0 pounds

6.5 pounds

7.5 pounds

6.5 is below the mean.

Explanation

6.5 is below the mean.

11) A baby has a z-score of -1.5 for weight. What is the baby’s actual weight?

8.85 pounds

5.55 pounds

6.60 pounds

7.00 pounds

7.2 + (-1.5 × 1.1) = 5.55 pounds.

Explanation

7.2 + (-1.5 × 1.1) = 5.55 pounds.

12) Two babies are born: Baby A weighs 8.3 pounds and Baby B weighs 6.1 pounds. Which statement is true?

Both babies have positive z-scores

Baby A has a positive z-score and Baby B has a negative z-score

Both babies have negative z-scores

Baby A has a negative z-score and Baby B has a positive z-score

8.3 > 7.2 (positive), 6.1

Explanation

8.3 > 7.2 (positive), 6.1

13) In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean (z-scores between -1 and 1)?

50%

68%

95%

99.7%

About 68% of data is within 1 SD.

Explanation

About 68% of data is within 1 SD.

14) A data value has a z-score of 3.2. What does this suggest?

This is a typical value

This value is slightly above average

This is an unusually high value, possibly an outlier

This value is below the mean

3.2 SDs above mean = very high.

Explanation

3.2 SDs above mean = very high.

15) If two different data sets have the same mean but different standard deviations, and you calculate z-scores for the same raw score in each set, what will be true?

The z-scores will always be the same

The z-scores will likely be different

The z-scores will both be zero

The z-scores cannot be calculated

Different SDs give different z-scores.

Explanation

Different SDs give different z-scores.

16) A student scores 670 on the SAT Math section. What is their z-score?

1.5

2.0

0.67

150

(670 − 520) ÷ 100 = 1.5

Explanation

(670 − 520) ÷ 100 = 1.5

17) What SAT Math score corresponds to a z-score of -0.8?

600

440

480

536

520 + (-0.8 × 100) = 440

Explanation

520 + (-0.8 × 100) = 440

18) Which z-score represents a student who scored below the mean?

Z = 0.5

Z = 1.2

Z = -0.3

Z = 0

Negative z = below average.

Explanation

Negative z = below average.

19) The heights of adult women in a population have a mean of 65 inches and a standard deviation of 3 inches. A woman who is 68 inches tall has a z-score of:

3.0

1.0

0.3

-1.0

(68 − 65) ÷ 3 = 1.0

Explanation

(68 − 65) ÷ 3 = 1.0