honors advanced algebra presentation 1-6. vocabulary
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Z-ScoresTRANSCRIPT
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Z-ScoresHonors Advanced Algebra
Presentation 1-6
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VocabularyZ-Score – the number of standard deviations from the mean. Used to tabulate the area under a normal curve.
- Sample meanμ – Population meanS – Sample standard deviationσ – Population standard deviation
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Z-ScoresA z-score is used to determine how many
standard deviations away a data point is from the mean.
Based on a z-score, we can determine probabilities of achieving certain goals.
Formula for calculating a z-score:
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Example 1Find the z-score of a data point of 21 when the mean is 24 and the standard deviation is 2
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Example 2Find the z-score of a data point of 58 when the mean is 50 and the standard deviation is 3.5
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Analyzing Z-ScoresZ-scores are interpreted from a z-score table.The table tells the area of the curve to the
left of a z-score.
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Example 3If a data point has a z-score of .5, what is the probability of getting lower than that score?
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Example 4If a data point has a z-score of -1, what is the probability of getting higher than that score?
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Example 5What is the probability of getting a score
between the z-score of -1 and the z-score of .5?
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Example 6Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8.1. Estimate the probability that a randomly
selected student scored less than an 87.
2. Estimate the probability that a randomly selected student scored more than a 79.
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Example 6 (cont’d)Scores on a test are normally distributed with a mean of 75 and a standard deviation of 8.3. Estimate the probability that a randomly selected student scored between 71 and 75.
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Example 7Heights of females are normally distributed with a mean of 5’4” with a standard deviation of 2.7 inches.1. What is the probability that a randomly
selected female will be shorter than 5’?
2. What is the probability that a randomly selected female will be taller than 6’?
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Example 7 (cont’d)Heights of females are normally distributed with a mean of 5’4” with a standard deviation of 2.7 inches.3. What is the probability that a randomly
selected female will be between 5’2” and 5’8”?
4. What is the probability that a randomly selected female will be either shorter than 5’2” or taller than 5’8”?
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Example 7 (cont’d)Heights of females are normally distributed with a mean of 5’4” inches with a standard deviation of 2.7 inches.5. If a female’s height gave her a z-score of 2.3, how tall was she?
6. If a female wants to be taller than 99.3% of other females, how tall does she have to be?