What is the probability of a 3 bag average falling between 9.08 and 9.16 ounces?

Question

A single 9 oz bag of chips has a N(9.12, .15) distribution

Answer 1

We need the Z-scores for the two limits:

Z₁=(9.08-9.12)/0.15=-0.2667; Z₂=(9.16-9.12)/0.15=0.2667.

Z₁=0.3949, Z₂=0.6051. So the difference is 0.2102 or 21.02%.

There's about a 21.02% probability that the average weight of 3 9oz bags of chips will lie between 9.08 and 9.16 ounces (within 0.04oz of the mean).