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Normal curve

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Normal curve

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    1. Normal curve

    2. Normal curve The curve is symmetric about the mean. Each half represents 50% of the total area. The total area is 1.0000 Areas can be thought of as probabilities. Areas could be written as percents. Areas can not be negative.

    3. Standard Normal curve The mean is 0. The standard deviation is 1.

    4. Format of the table The table has 2 halves – one for negative values of z and one for positive values of z. The left column tells the first decimal place for the z; the top row tells the second decimal place for z. We find the intersection of the row and column to find the area to the LEFT of z.

    5. Special notes For Z scores above 3.50, use the area of 0.9999 For Z scores below -3.50, use the area of 0.0001

    6. Reminder! Areas can never be negative. Z scores can be negative.

    7. Area under the Standard Normal Distribution Curve 1. To the left of any z value: Look up the z value in the table and use the area given.

    8. Area under the Standard Normal Distribution Curve 2. To the right of any z value: Look up the z value and subtract the area from 1.

    9. Area under the Standard Normal Distribution Curve 3. Between two z values: Look up both z values and subtract the corresponding areas.

    10. Example 1 Find the area to the left of z = 2.25

    11. Example 2 Find the area to the right of z = 1.50

    12. Example 3 Find the area between z = -1.35 and z = 2.15

    13. Your Turn Find the area for each: 1. area to the left of z = -1.04 2. area to the right of z = 1.07

    14. Your turn continued area between z = 0 and z = 2.75 area between z = -1.00 and z = 1.00

    15. Finding z given area Make sure the diagram shows the area to the left of the desired z score. Look in the body of the chart for the closest area, except for the special z scores. Read the z score.

    16. Example 4 The area to the right of z is 0.0250

    17. Example 5 The area from the mean to a positive z is 0.1628

    18. Example 6 The area from some negative z to the mean is 0.4772

    19. Your turn Find the z score for each: 5% is to the left of z 2. the top 15%

    20. Your turn continued P15 – Hint: P15 means 15% is lower than x 88% of the area is between –z and +z

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