Question

Carmen is a professor at a local university. In collecting data on her Introduction to Business course for a year, she wants to calculate the z-score for a student who scores a 83 on the final exam. The mean and the standard deviation scores on the exam are 72 and 5, respectively. Calculate the z-score.

Answer 1

Answer:

$\boxed {\boxed {\sf z=2.2}}$

Step-by-step explanation:

The z-score tells us how many standard deviations a value is away from the mean.

The formula is:

$z=\frac{x- \overline{x}}{s}$

where x is the value, $\overline {x}$ is the mean, and s is the standard deviation.

We want to find the z-score for the score of an 83, the mean is 72, and the standard deviation is 5.

$x=83 \\\overline {x}= 72 \\s=5$

Substitute the values into the formula.

$z=\frac{83-72}{5}$

Solve the numerator.

$z=\frac{11}{5}$

Divide.

$z=2.2$

The z-score is 2.2, which means the score of 83 is 2.2 standard deviations above the mean.