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= (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= (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