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Chapter 2: Q 2.2. (page 91)

Another student in the class, Brent, is 74 inches tall. How tall is Brent compared with the rest of the class? Give appropriate numerical evidence to support your answer.

Short Answer

Expert verified

Brent's height is 1.63 standard deviations above the mean.

Step by step solution

01

Step 1. Given

Dot plot of the class鈥檚 height distribution along with summary statistics from computer output.

02

Step 2. Concept

Value that has been standardized (z-score) The standardized value of xis z=x鈭�meanstandarddeviationif is an observation from a distribution with known mean and standard deviation. A z-score is a term used to describe a standardized value.

03

Step 3. Explanation

Ifxis an observation from a distribution that has known mean and standard deviation, so standardized score for xis, z=x鈭�mean/standarddeviation

As a result, it is stated that,

x=74

And, based on the dot plot provided, x=67and the standard deviation of the data Sx=4.29

z= 74鈭�674.29

z=1.63

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