STATISTICS 3N03/3J04
Test #2 * 2003-10-30
Aids permitted: any calculators and one sheet of notes (8.5" x 11", one side only).
Questions
1. Find the exact distribution for the total score when two fair four-sided dice are rolled independently. Plot the probability mass function and the cumulative distribution function for this distribution. Find the mean, median, mode, variance and standard deviation.
2. Here is a line of R code and its result. What does the code do? Taking the result to be a sample of observed data, draw a stem and leaf plot and find the sample mean, median, mode, variance and standard deviation.
> apply(matrix(sample(1:4, 20*2, repl=T), ncol=2), 1, sum)
[1] 6 6 3 3 6 8 2 4 3 6 5 5 7 5 3 3 5 7 5 6
3. If the weight of a pill is normally distributed with mean 50 g and standard deviation 1 g, and the pills are sold in boxes of 10 pills, what is the probability that at most 1 pill in a given box will weigh less than 48 g? If the pills are also sold in bottles of 1000 pills, what is the probability that at most 20 pills in a given bottle will weigh less than 48 g?
Note: F(2) = 0.97725, F(0.477) = 0.683
4. If the mean number of accidents at a given intersection were 3 per month over several years, would it be an unusual event if this month there were 6 or more accidents? Compute a probability to support your answer. State any assumptions you make.
5. Define the following terms: random variable, parameter.