Author Question: By law, a box of cereal labeled as containing 32 ounces must contain at least 32 ounces of cereal. ... (Read 112 times)

Mr3Hunna · **on:** Jul 24, 2018

By law, a box of cereal labeled as containing 32 ounces must contain at least 32 ounces of cereal.

The machine filling the boxes produces a distribution of fill weights that is mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.04 ounce. To ensure that most of the boxes contain at least 32 ounces, the machine is set so that the mean fill per box is 32.12 ounces. What percentage of the boxes do, in fact, contain at least 32 ounces?

Question 2

A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately mound-shaped and symmetric, with a mean of 61 jobs and a standard deviation of 8.

On what percentage of days do the number of jobs submitted exceed 69?

Mholman93 · **Reply #1 on:** Jul 24, 2018

Answer to Question 1

The value of 32 ounces falls three standard deviations below the mean. The Empirical Rule states that approximately all of the boxes will contain cereal amounts between 32.00 ounces and 32.24 ounces. Therefore, approximately 100 of the boxes contain at least 32 ounces.

Answer to Question 2

The value 69 falls one standard deviation above the mean in the distribution. Using the Empirical Rule, 68 of the days will have between 53 and 69 jobs submitted. Of the remaining 32 of the days, half, or 32/2 = 16, of the days will have more than 69 jobs submitted.