### Normal Curves Introduction

```+
Statistics: Chapter 6
Z scores review, Normal Curve Introduction
+
Do Now:

Complete the Beijing Olympics worksheet given to you when
you entered class.

This will be an extended do now and I will collect it. You may
work in table groups
+
Normal Models

Normal Models are appropriate for distributions whose
shape is uni-modal and symmetric.

“Bell shaped curve”
+
Symbols

N(mean, standard deviation)
The normal model with mean 0 and standard deviation of 1 is
called the standard normal model (or standard normal
distribution)
+
Symmetric Uni-Model Data

So we said that symmetric, unimodal data can be
standardized into a normal model….
1.
So don’t claim a normal model with skewed data.
2.
Is anything actually ever completely normal?
+
Normal Models

The 68 – 95- 99.7 Rule (Empirical Rule)
+
+
+
+ Sketch Normal Models using the 6895-99.7 Rule

Birth weights of babies N(7.6 lb, 1.3 lb)
+ Sketch Normal Models using the 6895-99.7 Rule

ACT Scores at a certain college, N(21.2, 4.4)
+
Do Now

Create a list in your calculator with the following numbers:

4
3
10
12
8
9
3
+
Calculating Standard Deviation on
a Calculator

Put all your data into a list

Under the STAT CALC menu, select 1-VAR STATS and hit
ENTER

Specify the location of your data, created a command like 1VAR STATS L1.

Hit ENTER again
+
Normal Models

The 68 – 95- 99.7 Rule (Empirical Rule)
+
+
Example: This is a practice

A forester measured 27 of the trees in a large wood that is up for
sale. He found a mean diameter of 10.4 inches and a standard
deviation of 4.7 inches. Suppose that these trees provide an
accurate description of the whole forest and the normal model
applies
+
N(36, 4)

What percent of data are between 32 and 40?

What percent above the mean are between 36 and 40?

What percent of data are between 28 and 44?

What range contains 99.7% of data?

What range contains 47.5% below the mean?

Where would the top 16% of data be?

What percent of data is outside 24 and 48?
+
Helmet Sizes
 The
army reports that the distribution of
head circumference among male soldiers is
approximately normal with a mean of 22.8
inches and a standard deviation of 1.1
inches.




What percent of soldiers have a head circumference greater than
23.9in?
A head circumference of 23.9 inches would be what percentile?
What percent of soldiers have a head circumference between
20.6 and 23.9inches?
What interval below the mean would contain 13.5% of soldiers?
+
Driving Speed

Suppose it takes you 20 minutes, on average, to drive to
school with a standard deviation of 2 minutes. Suppose a
normal model is appropriate for the distribution of driving
times.

How often will you arrive at school in less than 22 minutes?

How often will it take you more than 24 minutes?

Do you think the distribution of your driving times is unimodal
and symmetric in general?

Explain.
+
Practice

Try some on your own! As always, call me over if you are
confused!
+
Exit Ticket

A company that manufactures rivets believes the shear
strength (in pounds) is modeled by N(500, 50).

Draw and label the normal model (just sketch the curve)

Would it be safe to use these rivets in a situation requiring a shear
strength of 750 pounds? Explain.

About what percent of these rivets would you expect to fall below
900 pounds?

Rivets are used in a variety of applications with varying shear
strength requirements. What is the maximum shear strength for
which you would feel comfortable approving this company rivets?