Econ 310, Spring 2014- Week 7:
Problem 1 - An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of $27 and a standard deviation of $6.
1. What proportion of the bank's Visa cardholders pay less than $30 in interest?
2. What proportion pay more than $42 in interest?
3. What proportion pay less than $15 in interest?
4. What proportion pay interest in 1 standard deviation of mean? How about 2 standard deviation of mean?
Problem 2-
1. Let X ∼ N (3, 49), and that P(X > D) = 0.25. What is D?
2. Let Y ∼ N (µ, 49), and that P(Y < 3) = 0.75. What is µ?
3. Let M ∼ N (3, σ2), and that P(M > 4) = 0.4 What is σ?
Problem 3- The production of a complex chemical needed for anticancer drugs is exponentially distributed with 6 kilograms per hour.
1. What is the probability that the production process requires more than 15 minutes to produces the next 1 kilogram of drugs?
2. We know that the production was started 6 minutes ago, and it is not finished yet. What is the probability that the production process will not be finished in 15 minutes from now?
3. The factory has three separate production lines, which are operated independently. Suppose that the production time of drugs in each line has the same distribution as above. What is the probability that at least one of lines finish the production of 1 kilogram of drugs less than 15 minutes?