Download 5.1 Notes, AP Stat

5.1 Introduction to Normal Distributions
AP Statistics
Recall: Continuous Random Variable:
~
number of possible values
~represented by an
on a number line
~its probability distribution is called a
probability distribution
NORMAL DISTRIBUTION:
~
probability distribution for random variable,
~Used to model many
in nature, business, and industry
~Graph is called
PROPERTIES OF NORMAL DISTRIBUTION:
1.) Mean, Median, Mode are equal
2.) Normal curve is bell-shaped and
symmetrical about the mean
3.) Total area under the normal curve is 1
4.) Normal curve approaches, but never
touches, the x-axis as it extends farther
and farther away from the mean
5.) Between 𝜇 − 𝜎 and 𝜇 + 𝜎 (center of curve)
graph curves downward
Graph curves upward left of 𝜇 − 𝜎 and
right of 𝜇 + 𝜎
Points at which the curving changes from
downward to upward are called inflection
points.
~Graph is a probability density function: 𝑦 = 𝜎
x
2
2
1
𝑒 −(𝑥−𝜇) ⁄2𝜎
2𝜋
√
~Graphing Calculator!
~Two parameters, 𝜇 and 𝜎 completely determine shape of normal curve
~any mean and any positive standard deviation
~mean gives the location of the line of symmetry
~standard deviation describes the spread of the data
Example:
Which normal curve has the greatest mean?
Which normal curve has the greatest standard deviation?
Example: Use the normal curve to estimate the following:
Mean
Standard Deviation
Location of line of symmetry
Location of points of inflection
Normal Curves and Probability
Recall:
Example: Adult IQ scores are normally distributed with 𝜇 = 100 and 𝜎 = 15. Estimate the
probability that a randomly chosen adult has an IQ between 70 and 115.