Question

The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is Normal, with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. What weight should be put on the chocolate bar wrappers so that only 1% of bars are underweight?

Answer 1

Answer:

We are given:

$\mu=8.1, \sigma=0.1$

We have to first find the z value corresponding to area 0.01. Using the standard normal table, we have:

$z_{0.01}=-2.33$

Now using the z-score formula, we have:

$z=\frac{x-\mu}{\sigma}$

$-2.33=\frac{x-8.1}{0.1}$

$-0.233=x-8.1$

$x=8.1-0.233$

$x=7.867$ ounces.

Therefore, the weight that should be put on the chocolate bar wrappers so that only 1% of bars are underweight is 7.867 ounces.