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

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

The Normal Curve

EXAMPLE 1

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

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)

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.

a. Between 8 and 12 b. At most 6

c. At least 12 d. At most 14

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