Question

hw 3.2: z scores score: 0/6 answered: 0/3 question 1 on a recent quiz, the class mean was 73 with a standard deviation of 2.8. calculate the z - score (to 2 decimal places) for a person who received score of 81. z - score: is this unusual? not unusual unusual question help: message instructor

Explanation:

Step1: Recall Z - score formula

The formula for calculating the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Here, $x = 81$, $\mu=73$, and $\sigma = 2.8$.

Step2: Substitute values into the formula

Substitute the given values into the formula: $z=\frac{81 - 73}{2.8}=\frac{8}{2.8}\approx2.86$ (rounded to two decimal places).

Step3: Determine if the z - score is unusual

A z - score is generally considered unusual if its absolute value is greater than 2 (or sometimes 3, depending on the context). Since $|2.86|>2$, the z - score is unusual.

Answer:

Z - score: $\approx2.86$; Is this unusual? Unusual