Accurate labeling of packaged meat is difficult because of weight decrease resulting from moisture loss (defined as a percentage of the package’s original net weight). Suppose that moisture loss for a package of chicken breasts is normally distributed with mean value 4.0% and standard deviation 1.0%. (This model is suggested in the paper “Drained Weight Labeling for Meat and Poultry: An Economic Analysis of a Regulatory Proposal,” Journal of Consumer Affairs [1980]: 307–325.) Let x denote the moisture loss for a randomly selected package.

a. What is the probability that x is between 3.0% and 5.0%?

b. What is the probability that x is at most 4.0%?

c. What is the probability that x is at least 7.0%?

d. Find a number z* such that 90% of all packages have moisture losses below z*%.

e. What is the probability that moisture loss differs from the mean value by at least 1%?