Bottles of a popular cola contain a mean amount of 300 mL of cola. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. The distribution of the contents is normal with a standard deviation of 3 mL.

Question

a) What is the probability that one randomly selected bottle will contain less than
296 mL of cola?

b) What is the probability that the average of 6 randomly selected bottles will contain less than 296 mL of cola?.

Answer 1

Z= x-u/o
So,
296-300/3
= -.77
Look at a standard normal distribution table
.2794 is the value from the table.
If you draw the curve, you will know that the area is to the left.
So, you subtract:
.5000- .2794
=.2206 is the probability.
I am not sure about the second part.

Answer 2

b) Z = (score-mean)/SEm

SEm = SD/√n

Use same table.