The packaging process in a breakfast cereal company has been adjusted so that the average of m = 13.0 oz of cereal is placed in packages. Of course, not all packages have precisely 13.0 oz and the standard deviation of the actual weight is s = 0.1 oz and the distribution of weights is known to follow the normal probability distribution.
a) What proportion of the packages will contain more than 13.3 oz of cereal?
I know the following: Z = X-m/s = 13.3 - 13.0 / .1 = +3
So: P (x > 13.3) = P (Z > 3) = ? I don't know how to change the 3 into a proportion.
b) What proportion of the packages will contain less than 13.3 oz?
Z = X-m/s = 3. P (x < 13.3) = P(Z<3) = 1 - answer to a. Is this correct?
c. Calculate the 85th percentile and interpret the result. I know the answer is to the left of the 85th percentile but how do I find that?
d. Calculate the first quartile of this distribution. I don't know how to start.