Skip to lesson

Choose “Save as PDF” in the print dialog to keep a copy.

Cogito

Probability and Statistics · Chapter 6 · Lesson 1

Practice Worksheet

The Normal Distribution

The bell curve, and the rule that reads it.

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

NameDate

Figure — use these to answer the problems

A symmetric bell shape: tall in the middle, thin at both ends, with the two sides mirroring each other.
Low2
Mid-low7
Mid-high7
High2
Low2
Mid-low7
Mid-high7
High2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What percentage lies within one standard deviation of the mean?

    Answer

  2. Why does 2.5% lie above two standard deviations rather than 5%?

    • The 5% outside is split evenly between two tails.
    • It is a rounding adjustment.

  3. What percentage lies within two standard deviations?

    Answer

  4. What percentage lies within three standard deviations?

    Answer

  5. Mean 170, standard deviation 8. What value is two above the mean?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Mean 100, standard deviation 15. What value is one below the mean?

    Answer

  2. What percentage lies above the mean in a normal distribution?

    Answer

  3. What percentage lies outside one standard deviation?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each quantity by whether a normal model is reasonable.

    Write each item under the heading it belongs to: Adult heights · Measurement errors · Household income · Number of lottery wins per person

    Roughly normal

    Not normal

  2. Mean 50, standard deviation 5. What value is three above the mean?

    Answer

  3. The Middle

    What percentage lies within one standard deviation of the mean?

    Answer%

  4. The Tail

    What percentage lies more than two standard deviations above the mean?

    Answer%