AP Statistics: Section 2.2 A

One particularly important class of density curves are Normal curves

which describe Normal distributions. Normal curves are _________, _____________, and

__________. All Normal distributions have this same overall

shape.

symmetric single-peakedbell-shaped

The density curve for a Normal distribution is described by giving

its mean ____ (pronounced m-yew) and standard deviation ____ (lower case sigma). The mean is

located at the ________________ and is equal to the _______.

center of the curvemedian

Changing µ moves the Normal curve __________ without

changing its spread. The standard deviation, σ, controls the spread of

the Normal curve.

left or right

BCDA

We can locate by eye on the curve. As we move out in either direction from the center , the

curve changes from concave down (like a ______ ) to concave up (like

a ____ ). In advanced math courses, this point is called the

_________________.

frown cup

point of inflection

Normal distributions are important in statistics because:

1. Normal distributions are good descriptions for some distributions of ________.

Examples: scores on test taken by many people, like the __________; repeated careful measurements of the same quantity and characteristics of biological populations, such as ____________ and __________________.

real data

SAT or ACT

yields of corn lengths of pregnancies

2. Normal distributions are good approximations to the results of

some ________________.

Examples: the sum of the dots showing on 2 dice; the number of correct answers when guessing on

a T/F or multiple choice test

chance outcomes

3. Many statistical inferences based on Normal distributions work well for

other roughly symmetric distributions.

Caution: Many sets of data DO NOT follow a Normal distribution.

Example: personal income is strongly right-skewed

The 68-95-99.7 Rule (or Empirical Rule)In the Normal distribution with mean and

standard deviation :

approximately ________ of the observations fall within _______ of the mean .

approximately ________ of the observations fall within _______ of the mean .

approximately ________ of the observations fall within _______ of the mean .

%681%952%7.99

3

95% of the women’s heights lie between

_______________ and _______________

)5.2(25.64 inches 5.59

2(2.5)64.5inches 69.5

What percent of women aged 18 – 24, are between 62 and 67 inches tall? ______________%68

A woman aged 18 – 24, who is 72 inches tall is at what percentile? _______

A woman aged 18 – 24, who is 72 inches tall is at what percentile? _______

A woman aged 18 – 24, who is 72 inches tall is at what percentile? _______

A woman aged 18 – 24, who is 72 inches tall is at what percentile? _______

85.99P

The notation for the Normal distribution is . For example

3, the notation is __________.)5.2,5.64(N

),( N