1. X , Y and Z are independent random variables with E(X ) = 0, E(Y ) = 1, E(Z = 2) and SD(X ) = 1, SD(Y ) = 1 and SD(Z) = 2. (a) E(3 X +2Y +4Z) = (b) V D(4 X +2Y 3Z) = (c) SD(4 X +2Y 3Z) = (d) E(X Y Z) = (e) Calculate the SD(X Y )

2. The current age (in years) of 400 clerical employees at an insurance claims processing center is normally distributed with mean 38 and SD 6. (a) Are most of the employees at this center are older than 25? Why? (b) If none of these employees leaves the firm and no new hires are made, then the distribution a year from now will be normal with mean 39 and SD 7. (c) Three individuals are drawn at random from this population. What are the chances that the first person is older than the sample average of the second and third individuals?

3. The number of packages handled by a freight carrier daily is normally distributed. On average, 1,000 packages are shipped daily, with SD 200. Assume that the package counts are independent from one day to the next. (a) What is the distribution of the total number of packages shipped over five days? (b) What are the chances that the total number of packages shipped over five days is more than 6000? (c) What is the distribution of the sample mean of the number of packages shipped over ten days? (d) What are the chances that the sample mean of the number of packages shipped over ten days is more than 900? (e) What is the distribution of the difference between the numbers of packages shipped on any two consecutive days? (f) The difference between the numbers of packages shipped today and the number of packages shipped tomorrow is equal to zero. Would you agree to this statement?

(g) If each shipped package earns the carrier $10, then what is the distribution of the amount earned per day? (h) What are the chances that more packages are handled tomorrow than today?