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 μi 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