Which value is farther from the mean?

Question

During the winter months, a convenience store sells hot chocolate. Sales follow a normal distribution of mean=200 and standard deviation=210. Compare the z-scores of a single-day value of 250 cups with a 15-day average value of 120 cups. Which value is farther from the mean?

Answer 1

No biggie! The mean is the center, of course, and standard deviation is like a shoe-size; the step you take every time you walk further from the mean. Finally, the Z-score is the number of steps. We just need to use the formula:

Z = (X - μ) / σ

For the first data values:

Z = (250 - 200) / 210

   = 50 / 210

   = 0.238

For the second set:

Z = (120 - 200) / 210

   = -80 / 210

   = 0.381

It turns out the second set is further!