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Cogito

Probability and Statistics · Chapter 6 · Lesson 3

Practice Worksheet

Normal Probabilities and Percentiles

From a z-score to a proportion.

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

NameDate

Figure — use these to answer the problems

Slide the marker and think of the area to its left. That area is the percentile.
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5

Value5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Mean 100, sd 15, z = 1. What is the value?

    Answer

  2. What does the area to the left of a value represent?

    • The proportion of data below that value.
    • The proportion above it.

  3. z = 0. Percentile?

    Answer

  4. z = 1. Approximate percentile?

    Answer

  5. z = −1. Approximate percentile?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. 60% lies below a value. What proportion lies above, as a decimal?

    Answer

  2. Mean 200, sd 20, z = 2. What is the value?

    Answer

  3. Areas below two values are 0.84 and 0.16. What proportion lies between them?

    Answer

Stretch Yourself

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

4 problems

  1. Match each z-score with its approximate percentile.

    Draw a line from each item on the left to its match on the right.

    • z = −1
    • z = 0
    • z = 1
    • 16th
    • 50th
    • 84th

  2. Mean 70, sd 5, z = −2. What is the value?

    Answer

  3. The Median

    What percentile does z = 0 correspond to?

    Answer

  4. The Value

    Mean 500, sd 100, z = 1. What is the value?

    Answer