Chapter 5, Problem 96P

A previous study found that people consuming large quantities of vegetables containing lutein (mainly spinach) were less likely to develop macular degeneration, a common eye disease among older people (age 65+) that causes a substantial loss in visual acuity and in some cases can lead to total blindness. To follow up on this observation, a clinical trial is planned in which participants 65+ years of age without macular degeneration will be assigned to either a high-dose lutein supplement tablet or a placebo tablet taken once per day. To estimate the possible therapeutic effect, a pilot study was conducted in which 9 people 65+ years of age were randomized to placebo and 9 people 65+ years of age were randomized to lutein tablets (active treatment). Their serum lutein level was measured at baseline and again after 4 months of follow-up. From previous studies, people with serum lutein ≥ 10 mg/dL are expected to get some protection from macular degeneration. However, the level of serum lutein may vary depending on genetic factors, dietary factors, and study supplements.

(For the following problems, assume that lutein can be measured exactly, so that no continuity correction is necessary.)

Suppose that among people randomized to lutein tablets, at a 4-month follow-up the mean serum lutein level = 21 mg/dL with standard deviation = 8 mg/dL. If we presume a normal distribution for serum-lutein values among lutein-treated participants, then what percentage of people randomized to lutein tablets will have serum lutein in the therapeutic range?