103. The article “Computer Assisted Net Weight Control”

(Quality Progress, 1983: 22–25) suggests a normal distribution with mean 137.2 oz and standard deviation 1.6 oz for the actual contents of jars of a certain type. The stated contents was 135 oz.

a. What is the probability that a single jar contains more than the stated contents?

b. Among ten randomly selected jars, what is the probability that at least eight contain more than the stated contents?

c. Assuming that the mean remains at 137.2, to what value would the standard deviation have to be changed so that 95% of all jars contain more than the stated contents?