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Cogito

Probability and Statistics · Chapter 6 · Lesson 2

Practice Worksheet

z-Scores

How unusual is one value?

12 problems · about 21 minutes · TEKS P.S.3.B, S-ID.A.4

NameDate

Figure — use these to answer the problems

Mark a value and count standard deviations from the centre. That count is the z-score.
012345678910

7

Value7
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Value 90, mean 78, sd 6. What is the z-score?

    Answer

  2. Why can z-scores compare results from different tests?

    • A z-score has no units, so both are on the same scale.
    • Because all tests are marked out of 100.

  3. Value 85, mean 75, sd 5. z-score?

    Answer

  4. Value 70, mean 70, sd 4. z-score?

    Answer

  5. Value 55, mean 60, sd 10. z-score?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. z = 1.5, mean 100, sd 10. What is the value?

    Answer

  2. z = −1, mean 50, sd 8. What is the value?

    Answer

  3. Which z is more unusual? 1 for z = 0.4, 2 for z = −2.6.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the z-score comparison in order.

    Write 1 to 4 in the boxes to put these in order.

    • Subtract the mean from the value.
    • Divide by the standard deviation.
    • Repeat for the other distribution.
    • Compare the two z-scores.

  2. Value 92, mean 80, sd 6. z-score?

    Answer

  3. The Score

    Value 80, mean 70, standard deviation 5. What is the z-score?

    Answer

  4. The Below

    Value 60, mean 70, standard deviation 5. What is the z-score?

    Answer