**Find the mean and variance of the random variable**

**Question 1: **The uric acid values in free-disease adult males are approximately normally distributed with a mean and standard deviation of 5.7 and 1 mg percent, respectively, find the probability that a sample of size 9 will yield a mean:

(a) Greater than 6

(b) Between 5 and 6

(c) Less than 5.2

**Question 2: **Given a population in which Π = .6 and a random sample from this population of size 100, find the probability that the sample proportion:

(a) Greater than or equal .65

(b) Less than or equal .85

(c) Between .56 and .63 , inclusive.

**Question 3: **A random sample of size n = 35 is drawn from the pdf f(y) = 3(1-y2); 0 ≤ y ≤ 1. Use the central limit theorem to approximate………