Flashcards in Stat - Exam #1 Deck (134)

Loading flashcards...

121

## P (z

###
Probability that a standard normal random variable is...

LESSthan, or equal to, a

122

## P (a

###
Probability that a standard normal random variable is...

GREATER than, or equal to, a

123

## P (a

###
Probability that a standard normal random variable is...

BETWEEN a and b, INCLUSIVE

124

## Symmetry 1

###
Area LEFT of (-a) = Area RIGHT of (+a);

P (z

125

## Symmetry 2

###
Area LEFT of (-a) = (1 - Area RIGHT of +a);

P (z

126

## What is z-Sub-Alpha (z_apha)

###
The z-score such that the area under the standard normal curve is to the RIGHT of z_alpha = alpha;

EX: area under the curve to the right of Z_0.05 = 0.05

127

## What are the properties of the STANDARD NORMAL DISTRIBUTION?

###
1. Perfectly summetric, bell-shaped curve, with:

2. Mean zero (u=0) and standard deviation (sigma = 1);

3. Denoted: z

128

## What is the method to draw a Schematic (graphical) Normal Curve?

###
1. Draw a stylized normal curve;

2. Mark the positions of the z-score along the x-axis;

3. Shade in the area of interest;

-- Write z-value if known;

-- Write the area if known

129

## What is along the algebraic side of the Schematic Normal Curve?

###
Top = Area (Z-table)

Middle = Z (Z-trans)

Bottom = X (x-value)

130

## What is a z-table?

###
A table for the standard normal curve that gives...

1. z-scores in the margins, and

2. Area under the curve to the left of the z-score in the body

-- Note: ALWAYS look at the picture in the table;

-- Note: ALWAYS draw a schematic normal curve of the situation

131

## What will the z-table be used to find?

###
1. Area FROM a z-score, and

2. z-score FROM area

132

## What 3 situations utilize a z-table?

###
1. Away (from mean) = use AREA from table;

2. Across (mean) = Use 1-(z-table area);

3. Between (two z-scores) = Use schematic curve

133

## What is the method to find the area from an x-value?

###
1. Draw a schematic normal curve;

2. Shade the area of interest;

3. Mark the x-value known;

4. Convert the x-value to a z-score;

5. Get area from z-table

134