Warm - Up
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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