Hunter Chemical Company claims that its major product contains on the average 4.0 fluid ounces of caustic materials per gallon. It further states that the distribution of caustic materials per gallon is normal and has a standard deviation of 1.3 fluid ounces.
a. What proportion of the individual gallon containers for this product will contain more than 5.0 fluid ounces of caustic materials?
b. A government inspector randomly selects 100 gallon-size containers of the product and finds the mean weight of caustic material to be 4.5 fluid ounces per gallon. What is the probability of finding the mean of a sample of 100 that is 4.5 or greater? Do you think the production process was producing its usual level of caustic materials when this sample was taken?