1. A manufacturing process produces on the average two defective items per hour. What is the probability that after a defective item:
(a) One hour will pass before the next defective item?
(b) One-half hour will pass?
(c) Fifteen minutes will pass?
(d) What is the expected value and standard deviation of this distribution?
2. If a student has a grade point average 3 standard deviations above the mean in her school, what proportion of the other students in the school have:
(a) A higher grade point average?
(b) A lower grade point average?
3. According to Chebyshev's theorem, at least what proportion of the observations fall within
(a) 1.5 standard deviations from the mean,
(b) 2.5 standard deviations from the mean?