In Example 11.4 on page 516, we stated that, based on standards set by the United States Pharmacopeia (USP), a standard deviation of Xenical capsule weights of less than 2 mg is acceptable. We now ask you to obtain that result. In doing so, we presume that weights of Xenical capsules are normally distributed with a mean of 120 mg.
a. According to USP, the requirements for weight variation of capsules are met if each of the individual weights is within the limits of 90% and 110% of the mean weight. Find the lower and upper weight limits in order for USP requirements to be met.
b. Using statistical software, find the percentage of all possible observations of a normally distributed variable that lie within six standard deviations to either side of the mean.
c. Show that, if σ < 2, then fewer than two of every billion Xenical capsules will have weights that violate USP requirements.
d. Explain why a standard deviation of Xenical capsule weights of less than 2 mg is reasonably acceptable with respect to USP requirements.