The mean cholesterol levels of women age 45-59 in Kenya, Africa is 5.1 mmol/l and the standard deviation is 1.0 mmol/l. Assume that cholesterol levels are normally distributed.

(a) What is the random variable?

(b) Find the probability that a woman age 45-59 in Kenya has a cholesterol level above 6.2 mmol/l (considered a high level).

(c) Suppose doctors decide to test the woman’s cholesterol level again and average the two values.  Find the probability that this woman’s mean cholesterol level for the two tests is above 6.2 mmol/l.

(d) Suppose doctors being very conservative decide to test the woman’s cholesterol level a third time and average the three values.  Find the probability that this woman’s mean cholesterol level for the three tests is above 6.2 mmol/l.

(e) If the sample mean cholesterol level for this woman after three tests is above 6.2 mmol/l, what could you conclude?