GRAVETTER_CH06_Probability and the Normal Distribution Flashcards
TRUE OR FALSE: Although the exact shape for the normal distribution is defined by an equation, the normal shape can also be described by the proportions of area contained in each section of the distribution.
TRUE.
TRUE OR FALSE: Statisticians often identify sections of a normal distribution using variance.
FALSE.
It’s using z-scores.
REVIEW! What is the value of the mean and the standard deviation when any distribution is transformed into z-scores?
The mean has a value of 0, while the SD has a value of 1.
What table lists proportions of the normal distribution for a full range of possible z-score values?
Unit normal table
THINK! What are the two parts distinguished in a normal curve that is displayed by drawing a vertical line down the z-score of the curve?
The body (the larger section of the distribution) and the tail (the smaller section of the distribution)
THINK! What are four facets that the unit distribution table describes?
- z-score
- Proportion in body
- Proportion in tail
- Proportion between mean and z
TRUE OR FALSE: The body always corresponds to the larger part of the distribution whether it is on the right hand side or the left-hand side.
TRUE.
The same concept applies to the tail, which is always the smaller section, whether on the right-hand side or on the left-hand side.
TRUE OR FALSE: The proportions on the right-hand side of a normal curve are exactly the same as on the left-hand side, according to the unit normal table.
TRUE.
The numerical proportions are exactly the same.
Note, however, that for a negative z-score, the tail of the distribution would be on the left side and the body is in the right. For the positive, it would be reversed.
THINK! Since the unit normal table does not list negative z-scores, how do you find the proportions of a normal curve, given a negative z-score?
You must look up the corresponding proportions for the positive value of z.
TRUE OR FALSE: Proportions can be negative.
FALSE.
Proportions are always positive.
TRUE OR FALSE: Probability is equivalent to proportion.
TRUE.
TRUE OR FALSE: You can use the unit normal table to look up probabilities for normal distributions.
TRUE.
This is in accordance with the definition that probabilities are equivalent to proportions.
THINK! When using the unit normal (z) table, when a z-score is negative, why do the values for the tail and the body switch?
Note that this is the case because the only values found in the table are POSITIVE, and the z-scores given are NEGATIVE. The proportions are exactly the same, however, the values of the body and tail switch because of the signs.
Therefore, when looking for the proportions of a negative z-score, the answer must be derived through recalling that the proportions of the body and tail are switched, as compared to the positive z-score with the exact same value.
