normal distribution

Z Table and Associated Materials

  • Z table and Chapter 7 packet available for pickup.

  • Midterm test two due dates: all assignments due by class time on the 23rd.

Foundation for Section 7.2

  • Focus on finding z values as a precursor to solving problems.

  • Section 7.1 taught about standard normal distribution; Section 7.2 involves non-standard normal distributions.

  • Students need to use mean (bc) and standard deviation (c0) in Section 7.2.

Z Score Calculations

  • Z formula: z=x−μσz = \frac{x - \mu}{\sigma}

  • After finding z, do not stop at z value; must use z for area or probability calculations.

  • Correct usage of the z table is essential for determining area or probability.

    • Probability, area, and proportion are interchangeable terms.

Steps for Solving Problems in Section 7.2

  1. Find z: Use the z formula mentioned.

    • Round z to two decimal places immediately.

  2. Use the z table:

    • Determine area or probability based on z value.

    • Understand and interpret the 'less than' or 'greater than' nature of the problems.

  3. For probabilities greater than, use complement rule or switch z to find area.

  4. For between problems, find z for the upper and lower limits then subtract areas from the z table.

Special Note on Using the Table

  • Always refer to the z table may need to switch z sign when it's a greater than problem.

  • Draw sketches when applicable to visualize the distribution and area under the curve.

Common Mistakes to Avoid

  • Stopping after finding z.

  • Forgetting to round z correctly.

  • Misunderstanding probability and area terms.

  • Switching signs without proper justification.

Calculating x from z

  • When given area, use it to find z first, then use:
    x=μ+z⋅σx = \mu + z \cdot \sigma

  • Example: For areas such as the 60th percentile, recognize what area corresponds to.

Homework and Review

  • Homework focused on understanding how to calculate z and areas.

  • Chapter 7 covers sections 7.1 and 7.2, midterm review session to cover necessary materials from Chapters 5 to 7.

  • Practice using tables backward to find x values when given specific areas instead of z values.

  • Looking ahead to homework on number series involving sample sizes, treating n>1 in z calculations.