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Algebra II : Distributions and Curves

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Example Question #4 : Z Scores

In a normal distribution, if the mean score is 8 in a gymnastics competition and the student scores a 9.3, what is the z-score if the standard deviation is 2.5?

Possible Answers:

-1.04

0.52

2.16

-0.85

0.85

Correct answer:

0.52

Explanation:

Write the formula to find the z-score. Z-scores are defined as the number of standard deviations from the given mean.

$z=\frac{x-\mu}{\sigma }$

Substitute the values into the formula and solve for the z-score.

$z=\frac{x-\mu}{\sigma } = \frac{9.3-8}{2.5} =0.52$

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Example Question #8 : Z Scores

Suppose a student scored a on a test. The mean of the tests are , and the standard deviation is . What is the student's z-score?

Possible Answers:

-0.875

-1.143

-0.75

-0.85

-2.475

Correct answer:

-0.875

Explanation:

Write the formula for z-score where is the data, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

$z=\frac{x-\mu}{\sigma}$

Substitute the variables.

$z=\frac{65-72}{8} =- \frac{7}{8} = -0.875$

The z-score is: -0.875

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Example Question #5 : Z Scores

Suppose Bob's test score is 50. Determine the z-score if the standard deviation is 3, and the mean is 75.

Possible Answers:

$-\frac{75}{47}$

$-\frac{2}{3}$

$-\frac{25}{6}$

$-\frac{25}{3}$

Correct answer:

$-\frac{25}{3}$

Explanation:

Write the formula for z-scores. This tells how many standard deviations above the below the mean.

$z=\frac{x-\mu}{\sigma}$

Substitute the known values into the equation.

$z=\frac{50-75}{3} =-\frac{25}{3}$

The z-score is: $-\frac{25}{3}$

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Example Question #6 : Z Scores

Find the z-score if the result of a test score is 6, the mean is 8, the standard deviation is 2.

Possible Answers:

$\textup{The answer is not given.}$

Correct answer:

Explanation:

Write the formula to determine the z-scores.

$z=\frac{x-\mu}{\sigma}$

Substitute all the known values into the formula to determine the z-score.

$z=\frac{6-8}{2}$

Simplify this equation.

$z=\frac{-2}{2} = -1$

The answer is:

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Example Question #11 : Z Scores

Determine the z-score of a test result is 45, the mean is 60, and the standard deviation is 8.

Possible Answers:

$-\frac{15}{8}$

$\textup{There is not enough information to determine the z-score.}$

$-\frac{15}{16}$

$\frac{1}{8}$

$-\frac{15}{64}$

Correct answer:

$-\frac{15}{8}$

Explanation:

Write the formula for z-scores. Z-scores determine the number of standard deviations below or above the mean.

$z=\frac{x-\mu}{\sigma}$

Substitute the values into the formula to determine the z-score.

$z=\frac{45-60}{8}= -\frac{15}{8}$

The z-score is $-\frac{15}{8}$ .

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Example Question #12 : Z Scores

Suppose Billy scored a 54 on his exam. The mean of the exam grades is 66 and the standard deviation is 3. What is the z-score?

Possible Answers:

-3.75

Correct answer:

Explanation:

Write the formula for z-scores. Z scores determine how many standard deviations a score is above or below the mean.

$z=\frac{X-\mu}{\sigma}$

Substitute the known values in order to determine the z-score.

$z=\frac{X-\mu}{\sigma} = \frac{54-66}{3} = -4$

The answer is:

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Example Question #13 : Z Scores

Sarah scored an 8.5 out of ten on her gymnastics floor routine. If the mean of the scores is 9.2 and the standard deviation is 1.3, what is her z-score?

Possible Answers:

-1.268

-0.574

-0.642

0.338

-0.538

Correct answer:

-0.538

Explanation:

Write the formula for z-scores. Z-scores are indicators of how many standard deviations above or below the mean.

$z=\frac{x-\mu}{\sigma}$

$x=\textup{score}$

$\mu = \textup{mean}$

$\sigma =\textup{ standard deviation}$

Substitute the known values.

$z=\frac{8.5-9.2}{1.3} = \frac{-0.7}{1.3} = -0.538$

The answer is: -0.538

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Example Question #14 : Z Scores

You just took your ACT. The mean score was a with a standard deviation of . If you scored a , what is your z-score?

Possible Answers:

1.55

1.25

0.75

1.33

Correct answer:

1.33

Explanation:

Use the formula for z-score:

$z=\frac{x-\mu }{\sigma }$

Where is your score, $\mu$ is the mean, and $\sigma$ is the standard deviation.

$z=\frac{26-22}{3}=1.33$

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Algebra II : Distributions and Curves

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #4 : Z Scores

Example Question #8 : Z Scores

Example Question #5 : Z Scores

Example Question #6 : Z Scores

Example Question #11 : Z Scores

Example Question #12 : Z Scores

Example Question #13 : Z Scores

Example Question #14 : Z Scores

All Algebra II Resources

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