Question

A data set has a mean of 150 and standard deviation of 13. The unusual values are those that are less than

Answer 1

Using z-scores, it is found that the unusual values are those that are less than 124.

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The z-score of a measure X in a data-set with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations X is from the mean.
• Measures that are more than 2 standard deviations from the mean are unusual.
• Z < -2 means that the measure X is unusually low.
• Z > 2 means that the measure X is unusually high.

In this problem:

• Mean of 150, thus $\mu = 150$.
• Standard deviation of 13, thus $\sigma = 13$.

$Z = \frac{X - \mu}{\sigma}$

$-2 = \frac{X - 150}{13}$

$X - 150 = -2(13)$

$X = 124$

Unusual values are those that are less than 124.

A similar problem is given at brainly.com/question/15315313