Determine and Interpret Z-Scores
-A Severe Drought Affected Several Western $\begin{array} { l l l l l l l l l l l l l } 60 & 57 & 62 & 69 & 46 & 54 & 64 & 60 & 59 & 58 & 75 & 51 & 49 \end{array}$

question 153

Multiple Choice

Determine and Interpret z-Scores
-A severe drought affected several western states for 3 years. A Christmas tree farmer is worried about the drought s effect on the size of his trees. To decide whether the growth of the trees has been retarded, the farmer decides to take a sample of the heights of 25 trees and obtains the following results (recorded in inches) : $\begin{array} { l l l l l l l l l l l l l } 60 & 57 & 62 & 69 & 46 & 54 & 64 & 60 & 59 & 58 & 75 & 51 & 49 \end{array}$
$\begin{array} { l l l l l l l l l l l l } 60 & 57 & 62 & 69 & 46 & 54 & 64 & 60 & 59 & 58 & 75 & 51 \\ 67 & 65 & 44 & 58 & 55 & 48 & 62 & 63 & 73 & 52 & 55 & 50 \end{array}$
$\begin{array} { l l l l l l l l l l l l } 67 & 65 & 44 & 58 & 55 & 48 & 62 & 63 & 73 & 52 & 55 & 50 \end{array}$ The tree farmer feels the normal height of a tree that was unaffected by the drought would be 65 inches. Find the z-score for a tree that is 65 inches tall.

• A) \(z = 0.84\)
• B) \(z = 0.98\)
• C) \(z = 0.77\)
• D) \(z = 0.98\).

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Definitions:

Standard Deviation

A measure of the amount of variation or dispersion of a set of values, indicating how much the values in a data set differ from the mean.

Dinner Cost

The total expense associated with a evening meal, including food, beverages, taxes, and tips.

Normal Distribution

A probability distribution that is symmetric around its mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Standard Deviation

A parameter that captures the level of scattering or variation among values in a dataset.