Help with statistics homework/Central Limit Theorem?

Question

I'm stuck on a particular problem and was wondering if anybody could help me out...

1. Let "x" be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12-hour fast. Assume that for people under 50 years old, "x" has a distribution that is approximately normal with mean = 85 and estimated standard deviation = 25. A test result "x" < 40 is an indication of severe excess insulin, and medication is usually prescribed.

a. What is the probability that, on a single test, "x" < 40?
b. Suppose a doctor uses the average x-bar for two tests taken about a week apart. What can we say about the probability distribution of x-bar? What is the prob. that "X" < 40?
c. Repeat part b for n=3 tests taken a week apart.
d. Repeat part b for n = 5 tests taken a week apart.


I'd really appreciate it if you could help out. I've asked all my other classmates and searched the web but had no luck.

Answer 1

for part a, first figure out the z-value: (40-85)/25=-1.8 look the corresponding probablility up for this value in a z table.
b. The mean would stay the same but the standard deviation would be 25/sqrt(2)=17.67
c. new standard deviation= 25/sqrt(3)
d. new standard deviation = 25/sqrt(5)

For c and d you just compute the z-value based on the mean of 85 and the new standard deviation.