Question 3 (10 marks)\ Let

x_(1),x_(2),dots,x_(n)

form a random sample of size

n

from some probability distribution with mean\

\\\\mu

and variance

\\\\sigma ^(2)

. If

n

is greater than 60 ,\ (a) What is the distribution of sample mean? Explain.\ (b) Compute the probability that the sample mean is exactly 2.\ (c) Compute the probability that the sample mean is within

\\\\mu +-1.6\\\\sigma _(\\\\bar{x} )

.

Question 3 (10 marks) Let X1,X2,,Xn form a random sample of size n from some probability distribution with mean and variance 2. If n is greater than 60 , (a) What is the distribution of sample mean? Explain. (3 marks) (b) Compute the probability that the sample mean is exactly 2. (2 marks) (c) Compute the probability that the sample mean is within 1.6x