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Flashcards in Stat - Exam #1 Deck (134)
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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

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

1. Draw a schematic normal curve;
2. Shade the area of interest;
3. Mark know area;
4. Get z-score from z-table;
5. Convert z-score to x-value