Section 6.2PART 1

STATISTICS

MondayFebruary 24

• Notes – Section 6.2 PART 1 Standard Units and Areas Under the Standard Normal Distribution

• Homework due Tuesday:A#6.21 pages 256 – 258 #8 - 28 even

Section 6.2 – Standard Units and Areas Under the Standard Normal

DistributionsAfter this section, you will be able to:

1. Convert raw data to z scores;

2. Convert z scores to raw data;

3. Graph the standard normal distribution and find areas under the standard normal curve.

Differences in Normal Distributions

1. The mean may be located anywhere on the ________________________,

and

2. The ______________________________ may be more or less spread

according to the size of the

__________________________________________________.…causes difficulties when computing the ______________ under the curve in a specified interval of x values

z Scores

The z value or z score give the number of

_____________________________ between the _____________________

measurement x and the ____________________of the x distribution.

x Values and Corresponding z ValuesX Value in Original

DistributionCorresponding z

Value or Standard Unit

Example: Standard ScoreLittle Bambinos pizza franchise specifies that the average amount of cheese on a large pizza should be 8 ounces and the standard deviation only 0.5 ounce. An inspector picks out a large pizza at random in one of the pizza parlors and finds that it is made with 6.9 ounces of cheese. Assume that the amount of cheese on a pizza follows a normal distribution. If the amount of cheese is below the mean by more than three standard deviations, the parlor will be in danger of losing its franchise.

How many standard deviations from the mean is 6.9? Is the pizza parlor in danger of losing its franchise?

Raw Scores

Given an x distribution with __________ and ____________________________,

the raw score x corresponding to a z score is:

PRACTICE: Standard Score and Raw Score

Rod figures that it takes an average (mean) of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to an early-morning class.

A. One day it took Rod 21 minutes to get to class. How many standard deviations from the average is that? Is the z value positive or negative? Explain why is should be either positive or negative.

B. What commuting time corresponds to a standard score of ? Could Rod count on making it to class in this amount of time or less?

The Standard Normal Distribution

Table 5 – Appendix II• Pages A22 and A23 in your text

• Left-tail style table

PRACTICE: Standard Normal Distribution Table

Use Table 5 of Appendix II to find the described areas under the standard normal curve.

a. Find the area under the standard normal curve to the left of

Insert table 6-3

Insert fig 6.16

b. Find the area to the left of .

PRACTICE: Standard Normal Distribution Table

Insert fig 6.17

Insert table 6-4

PRACTICE: Using the Standard Normal Distribution Table

Looking at Table 5 in Appendix II:

a. As z values increase, do the areas to the left of z increase?

b. If a z value is negative, is the area to the left of z less than 0.5000?

c. If a z value is positive, is the area to the left of z greater than 0.5000?

Finding areas other than to the left1. For areas to the left of a specified z value, __________________________________________

2. For areas to the right of a specified z value, _________________________________________

3. For areas between two z values, and (where ) _______________________________

Hints:• Round or format z values to 2 decimal places before using the

table• Treat any area to the left of a z value smaller than -3.49 as

0.000• Treat any area to the right of a z value greater than 3.49 as

1.000

Insert fig 6-18

PRACTICE: Using the Standard Normal Distribution Table

Use Table 5 of Appendix II to find the described areas under the standard normal curve.

a. Find the area between and

PRACTICE: Using the Standard Normal Distribution Table

Use Table 5 of Appendix II to find the described areas under the standard normal curve.

b. Find the area to the right of

Section 6.2PART 2

STATISTICS

TuesdayFebruary 25

• Warm-up – Page 257 #9• Check in and go over A#6.21

• Notes – Section 6.2 – PART 2 Probabilities associated with the Standard Normal Distribution

• Homework due Wednesday:A#6.22 pages 256 – 258 #1-7 all; 30-48 even

WARM-UP: Page 257 # 9

PRACTICE: Using the Standard Normal Distribution Table

Let z be a random variable with a standard normal distribution.

a. refers to the probability that z values lie to the right of 1.15. Shade the corresponding area under the standard normal curve and find

PRACTICE: Using the Standard Normal Distribution Table

Let z be a random variable with a standard normal distribution.

b. Find . First, sketch the area under the standard normal curve corresponding to the area.