Empirical Rule as it Relates to Normal Distribution Scenario analysis help

Scenario Script Caption: Production at the Burlington facility of the Princess Foods Corporation has been found

to occur at a normal distribution. While some weeks are extremely productive and others fall far

enough below the average to be considered especially unproductive, production generally

follows the pattern of a bell curve.

Bonnie: I'm still concerned that the quality control issues will cause production to drop too low.

We have another board meeting in a few weeks. If production dips that week, we are in bad

shape.

Caption: Depending on the timing, an off week could have an inordinately large impact on the

business if that bad week is enough to make shareholders skittish.

Bonnie: Can you to do some research on the probability that production will stay above targets

on any given week?

Question:include the raw data and a clear interpretation of the data that justifies your findings

Use the empirical rule to draw conclusions about the data set below assuming a normal

distribution and to determine the probability of Modules produced per week at Princess Foods

Corporation.

Production has been determined to be a normal distribution

Average production is 12,000 Modules per week with a standard deviation of 600

Answer the following questions:

1. What is the probability that next week's production is between 11,400 to 13,200?

2. What is the probability that next week's production be less than10,200?

3. What is the probability that next week's production is between 12,600 and 13,800?