from Math IIIREVIEWING NORMAL DISTRIBUTIONS AND

Z-SCORES

You will need:• White board &

marker• Calculator• Z-score Table• FFM Sheet

(eventually)

The Standard Normal Distribution is a normal distribution with a mean of 0 and a standard deviation of 1. To more easily compute the probability of a particular observation given a normally distributed variable, we can transform any normal distribution to this standard normal distribution using the following formula:

; ; When you fi nd this value for a given value, it is referred

to as the z-score. The z-score is a standard score for a data value that

indicates the number of standard deviations that the data value is away from its respective mean.

REMINDER:

a.) What data value corresponds to a z-score of 1.5?

1.) GIVEN A NORMAL DISTRIBUTION WITH A

b.) What data value corresponds to a z-score of ?

1.) GIVEN A NORMAL DISTRIBUTION WITH A

Calculate the z-score for:

a.) X = 65

2.) GIVEN A NORMAL DISTRIBUTION WITH A

Calculate the z-score for:

b.) X = 90

2.) GIVEN A NORMAL DISTRIBUTION WITH A

Calculate the z-score for:

c.) X = 82.5

2.) GIVEN A NORMAL DISTRIBUTION WITH A

Determine the X value which corresponds to the following z-scores:

a.) Z =

HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

3.) GIVEN A NORMAL DISTRIBUTION WITH A

Determine the X value which corresponds to the following z-scores:

b.) Z = 0.75

HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

3.) GIVEN A NORMAL DISTRIBUTION WITH A

Determine the X value which corresponds to the following z-scores:

c.) Z = 1.9

HINT: You will need to work backwards to find X…plug values into z-score formula and solve for x.

3.) GIVEN A NORMAL DISTRIBUTION WITH A

Using the empirical rule,

a.) what percent of the data falls between and ?

b.) what x-values would correspond to (a) to contain that same percentage of data?

4.) GIVEN A NORMAL DISTRIBUTION WITH A

Using the empirical rule,

c.) what percent of the data falls between and ?

d.) what x-values would correspond to (c) to contain that same percentage of data?

4.) GIVEN A NORMAL DISTRIBUTION WITH A

Using the empirical rule,

e.) What percent of the data falls to the LEFT of ?

4.) GIVEN A NORMAL DISTRIBUTION WITH A

Using the empirical rule,

f.) What percent of the data falls to the LEFT of ?

4.) GIVEN A NORMAL DISTRIBUTION WITH A

Using the empirical rule,

g.) What percent of the data falls to the RIGHT of ?

4.) GIVEN A NORMAL DISTRIBUTION WITH A

In a normal distribution with and ,

1.) find X if 2.) find P() = _____ 3.) P 48.2)

FFM 8/16/13:

Section 9.2, pg. 588-590# 9.20#9.22#9.24#9.28

A.M. III HOMEWORK