Question

a collection of temperature values has mean 82.25 degrees and standard deviation 11.78 degrees. suppose that saturdays temperature was 94 degrees. find and interpret the z - value you found in part a. in terms of the setting of this question. saturdays temperature was 1.00 standard deviations above the mean for this exam. (round to two decimal places as needed.)

Explanation:

Step1: Recall z - value formula

The formula for the z - value is $z=\frac{x-\mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Identify values

We are given that $\mu = 82.25$, $\sigma=11.78$, and $x = 94$.

Step3: Calculate z - value

$z=\frac{94 - 82.25}{11.78}=\frac{11.75}{11.78}\approx1.00$

The z - value of 1.00 means that Saturday's temperature of 94 degrees is 1.00 standard deviations above the mean temperature of 82.25 degrees for the collection of temperature values.

Answer:

Saturday's temperature was 1.00 standard deviations above the mean.