1.A random variable X is normally distributed with a mean of 121 and a variance of 121, and a random variable Y is normally distributed with a mean of 150 and a variance of 225. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable below.

W=8X7Y

W= an integer or adecimal.)

2W= ( an integer or adecimal.)

2.A random sample of 81 items is selected from a population of size 310. What is the probability that the sample mean will exceed 204 if the population mean is 200 and the population standard deviation equals 20? (Hint: Use the finite population correction factor since the sample size is more than5% of the populationsize.)

Px>204=

(Round to four decimal places asneeded.)

3.An author receives a contract from apublisher, according to which he is to be paid a fixed sum of $8,000 plus $1.75 for each copy of his book sold. His uncertainty about total sales of the book can be represented by a random variable with a mean of 30,000 and a standard deviation of 7,500. Find the mean and standard deviation of the total payments he will receive.

The mean of the total payments he will receive is $.

The standard deviation of the total payments he will receive is $.