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 standard deviations 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

Substitute the values into the formula: $z=\frac{94 - 82.25}{11.78}=\frac{11.75}{11.78}\approx1.00$.

Step4: Interpret z - value

A positive z - value means the data - point is above the mean. The z - value of approximately 1.00 means that Saturday's temperature was 1.00 standard deviations above the mean temperature of the collection.

Answer:

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