Empirical Rule & Z-Scores

Front

What does a positive z-score indicate about a data point's location relative to the mean?

Back

A positive z-score indicates that the data point is above the mean.

Front

What does a negative z-score indicate about a data point's location relative to the mean?

Back

A negative z-score indicates that the data point is below the mean.

Front

What is the z-score for a data point that is 2 standard deviations below the mean?

Back

The z-score is -2.00.

Front

According to the Empirical Rule, what percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

95% of the data falls within 2 standard deviations of the mean.

Front

What does it mean if a distribution is skewed to the right?

Back

A right-skewed distribution has a longer tail on the right side, indicating that there are a few high values.

Front

How do you calculate the z-score for a given data point?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation.

Front

In the context of track performance, what does a lower z-score indicate?

Back

A lower z-score indicates better performance, as it means the athlete's time is further below the mean.

Front

What is the mean and standard deviation of Emmett's 400m run?

Back

The mean is 51 seconds and the standard deviation is 3 seconds.

Front

What is the mean and standard deviation of Reese's 800m run?

Back

The mean is 2 minutes 46 seconds (or 166 seconds) and the standard deviation is 15 seconds.

Front

What were Emmett's and Reese's z-scores for their respective events?

Back

Emmett's z-score was +0.83, and Reese's z-score was -3.0.