7.2 The Normal Distribution

The Normal Distribution is a unimodal, symmetric, mound shaped probability density curve with the following properties:

• The mean, median, and the mode are all equal

• is the equation of the curve

• 68% of the data appears within 1 standard deviation of the mean, 95% of the data appears within 2 standard deviation of the mean, 99.7% of the data appears within 3 standard deviations of the mean

Ex 1 Giselle is 168 cm tall. In her high school, boys heights are normally distributed with a mean of 174 cm and a standard deviation of the 6 cm. What is the probability that the first boy Giselle meets at school tomorrow will be taller than she is?

Ex 2 p. 426 ex 2:

x is mass of sparkle in each bag

Find the z-score:

Find the area under the curve:

Consult the z table of p. 606. Start with the columns and find the -1.6 part, then go across until you are lined up with the 0.07 part.

Ex 3 p. 428 ex 3

Test score is out of 750

Her score = 655, is she in the top 25%?

Method 1

Since her score is greater than 1 std dev from the mean, then she is above 50% plus 32% of the scores. (Diagram may be required.) So she got in.

Method 2

Once you have the z-score, use the z table and find that she scored at just below the 95^th Percentile.

Method 3

Use the z table backward. Find the number on the chart that is closest to 0.75, find the z score associated with it. At 75%, the z score is approximately 0.67, well below her z score.

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