Empirical Rule & Z-Scores Flashcard

Front

In a normal distribution, what percent of the values lie above the mean?

Back

50% of the values lie above the mean in a normal distribution.

Front

What is the Z-score for a value that is below the mean by 2 standard deviations?

Back

The Z-score is -2.00 for a value that is below the mean by 2 standard deviations.

Front

How do you calculate the Z-score?

Back

Z-score = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What is the Z-score for Paula if she got 1400 on the SAT, the mean was 1100 and the SD was 275?

Back

The Z-score for Paula is +1.09.

Front

What percentage of data is within 3 standard deviations in a normal distribution?

Back

99.7% of the data is within 3 standard deviations in a normal distribution.

Front

In a normal distribution, what percent of the values lie within 1 standard deviation of the mean?

Back

Approximately 68% of the values lie within 1 standard deviation of the mean.

Front

What is the empirical rule?

Back

The empirical rule states that for a normal distribution: 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

Front

If a factory's weight of concrete poured follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds, what interval contains approximately 95% of the weights?

Back

The interval is approximately 1106 to 1194 pounds.

Front

What does a Z-score of +1.00 indicate?

Back

A Z-score of +1.00 indicates that the value is 1 standard deviation above the mean.

Front

What does a Z-score of -1.00 indicate?

Back

A Z-score of -1.00 indicates that the value is 1 standard deviation below the mean.