Question 1: The uric acid values in free-disease adult males are approximately normally distributed with a mean and standarddeviation 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 

P(1/8 < Y < 3/8)

Question 4: Let X'_i be the sample mean of a simple random sample drawn from a population having mean μ_i and variance σ² for i = 1,2.

(a) Find the mean and variance of the random variable x'₁ - x'₂, for both cases, with and without replacement.

(b) Assuming that both populations are normally distribution, what is the type of the probability distribution of X'₁ - X'₂

(c) Suppose the both population have unknown distributions but both samples are greater than 30. Could you approximate the distribution of X'₁ - X'₂ ? Explain.

Question 5: A random sample of size n =35 is drawn from the pdf f(y) = 3(1-y)²; 0 ≤ y ≤ 1. Use the central limit theorem to approximate P(1/8 < Y' < 3/8)

Question 6:

A randomsample of size n = 9 is drawn from a normal distribution with mean 32.5 and variance 2.25, find the constants 32.5 and 2.25 so that:

P(a < x' < b) = 0.95