Algebra II : Distributions and Curves

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #7 :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:

Correct answer:

Explanation:

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

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

Example Question #8 :Z Scores

Suppose a student scored aon a test. The mean of the tests are, and the standard deviation is.学生的z分数是多少?

Possible Answers:

Correct answer:

Explanation:

Write the formula for z-score whereis the data,is the population mean, andis the population standard deviation.

Substitute the variables.

The z-score is:

Example Question #9 :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:

Correct answer:

Explanation:

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

Substitute the known values into the equation.

The z-score is:

Example Question #10 :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:

Correct answer:

Explanation:

Write the formula to determine the z-scores.

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

Simplify this equation.

The answer is:

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:

Correct answer:

Explanation:

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

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

The z-score is

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:

Correct answer:

Explanation:

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

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

The answer is:

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:

Correct answer:

Explanation:

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

Substitute the known values.

The answer is:

Example Question #14 :Z Scores

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

Possible Answers:

Correct answer:

Explanation:

Use the formula for z-score:

Whereis your score,is the mean, andis the standard deviation.

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