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Warm - Up

Warm - Up. Two foot ball teams scored the following points during a game. Which team is more consistent? On average witch team scores the most points? Team A: 14, 21, 21, 7, 14, Team B: 7, 28, , 21, 7, 14. Normal Distribution.

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Warm - Up

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  1. Warm - Up Two foot ball teams scored the following points during a game. Which team is more consistent? On average witch team scores the most points? Team A: 14, 21, 21, 7, 14, Team B: 7, 28, , 21, 7, 14

  2. Normal Distribution

  3. Normal distribution- is modeled by a bell-shaped curve called a normal curve. • The normal curve is symmetric about the mean, and the total area under the curve is 1. • A normal distribution has a mean x and a standard deviation σ

  4. The Normal Curve

  5. Example 1 • Sketch the normal curve that has a mean (x) of 10 and a standard deviation(σ) of 2.

  6. Example 2 • A normal distribution has mean x and standard deviation σ. Find the indicated probability of a randomly selected x-value from the distribution. • 1. P(x ≤ x + σ) • 2. P(x ≤ x ≤ x+ σ) • 3. P(x ≥ x+ σ)

  7. Example 3 • A normal distribution has a mean of 10 and a standard deviation of 2. Find the probability that a randomly selected x-value from the distribution is in the interval. • Between 8 and 12 b. At most 6 c. At least 12 d. At most 14

  8. The Empirical Rule • Empirical Rule is as follows: • If a distribution is normal, then approximately: • 68% of the data will be located within one standard deviation symmetric to the mean • 95% of the data will be located within two standard deviations symmetric to the mean • 99.7% of the data will be located within three standard deviations symmetric to the mean

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