Question

Suppose a manufacturer makes disposable peppercorn grinders. the number of peppercorns in the grinders is normally distributed with a mean of 322 peppercorns and a standard deviation of 5.3 peppercorns. suppose the manufacturer will only sell peppercorn grinders with a z-score between –0.9 and 0.9. what are the least and most peppercorns a grinder can contain

Answer 1

We will translate each z-score in turn into X

for z-score=$-0.9$
$-0.9= \frac{X-322}{5.3}$
$-0.9*5.3=X-322$
$-4.77=X-322$
$X=-4.77+322=317.23$≈317 (to the nearest integer)

for z-score=$9$
$9= \frac{X-322}{5.3}$
$9*5.3=X-322$
$47.7=X-322$
X=47.7+322=369.7 ≈ 367 (to the nearest integer)

The least number of peppercorns is 317
The most number of peppercorns is 367