MATH 367, spg 98, CHAPTER 5 Extra Problems

1. Suppose it is known that the number of items produced in a certain factory during a week is a random variable with mean 50 and standard deviation 5. What can be said about the probability that this week’s production will be between 40 and 60?

2. Let X_{i} be the number of items produced in a certain factory during the ith week of 1997. By previous experience, it is known that variance is 25. If you know that X_{1}+X_{2}+…+X_{52} = 2664, what can you say about the common mean m = E(X_{i}), i = 1, 2, …, 52?

3. If Var(X) = 0, what can you say about X?

4. If 10 fair dice are rolled, find the approximate probability that the sum obtained is between 30 and 40.

5. If X is a random variable with E(X) = σ^{2} = 20, what can you say about P (0 < X < 40)?

6. Let X_{1}, …, X_{20} be independent random variables with mean 1 and variance 1. What can you say about P (X_{1} + … + X_{20} > 15)?