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Week 8 Vocabulary Summary
Section 5.1 – Introduction to Norma Distribution and the Standard Normal
Distribution
Properties of a Normal Distribution
 The mean, median, and mode are equal
 The normal curve is bell-shaped and is symmetric about the mean
 The total area under the normal curve is equal to one
 The normal curve approaches, but never touches, the x-axis as it extends farther and farther
away from the mean.
The Inflection points (where the curve changes from curving upward to curving downward) are

located at   1 ( mean + or – 1 standard deviation.
To convert any x value from a normal distribution to a standard normal distribution use z-score
Formula
z
value  Mean
x
or
SD

Properties of a standard normal distribution
 The cumulative area is close to 0 for z-score close to z = -3.49
 The cumulative area increases as the z-scores increase
 The cumulative area for z= 0 is 0.5000
 The cumulative area is close to 1 for z-scores close to z= 3.49
Finding the Area under the standard Normal Curve given a z-score
Step 1: Sketch the curve
Step 2 : decide if the problem is <= x, >x, or between xl and xu.
Using the Standard normal table
Look up the z value in the Standard Normal Table (This will give the area to the left of the z
score.
If need to find >x , find 1 – the area found in step 3
If need to find the area between to z-scores, subtract the smaller area from the larger.
Using TI 83- 84
For area < x, normalcdf [-10000, x]
For area >x, normalcdf[x, 10000]
For area between lower and upper values, normalcdf [lower x, upper x]
Using Excel
For area < x, NORMDIST(z-score)
For area >x, 1- NORMDIST(z-score)
For area between lower and high, NORMDIST(z-score{high}) - NORMDIST(z-score{low})
Section 5.2 – Normal Distribution: Finding Probabilities
Finding Probability ≤ x
Step 1: Convert raw scores (x) to z-values
z
x

Step 2
BY HAND: Obtain areas from the table.
BY Excel function
See above
BY TI 83
See above
Finding Probability ≥ x
BY HAND
Step 1: Convert raw scores (x) to z-values
z
x

Step 2
BY HAND: Obtain areas from the table to the left of x, and then find 1 – P( < x)
BY Excel function
See above
BY TI 83
See above
Finding xl ≤ Probability ≤ xu
BY HAND
Step 1: Convert raw scores (x) to z-values
Step 2: Rewrite the single interval as a difference
Step 3:
BY HAND: Obtain areas from the table to the left of x, and then take the difference
BY Excel function
See above
BY TI 83
See above
Section 5.3 – Normal Distribution: Finding Values
(going the opposite direction from 5.2)
A: Given an area, find the z-score.
BY HAND: Find the area in the body of the table
Read the row and column as the z- score.
BY Excel function
NORMSINV(area)
BY TI 83
invNorm[area)
Transforming a z-score to an x-value
z
x

Use the formula but solve for x
The simplified version of this is
x    z
Finding a Specific Data Value for a Given Probability
Step 1: Sketch a graph
Step 2: Find the z-score that corresponds to the given area. A: above
Step 3: Find x using the equation
Step 4: Interpret the results
x    z