· Write your name in the upper right (stapled) corner on the back of the test.
· Show your work. Clearly indicate your final answer.
· Carry out all calculations to at least 3 significant figures (unless they terminate sooner).
· You may use 1 sheet of notes, a calculator, and the tables in the back of the textbook.
· Numbers in brackets [ ] indicate how much a problem is worth.
1. [20] The FORTE satellite records data on lightning strikes. Suppose that, while the satellite is over a particular region, detectable lightning strikes are occurring at an average rate of 1 strike every 2 minutes.
(a) [4] Because FORTE is moving in orbit, it can only observe this region for a 10-minute period. Let X = the number of detectable lightning strikesduring a 10-minute period. What type of random variable is X? (Circle one letter.)
A. Poisson
B. Uniform
C. Binomial
D. Exponential
E. Normal
(b) [6] Find .
(c) [4] Let T = the length of time (in minutes) for the first detectable lightning strike to occur. What type of random variable is T? (Circle one letter.)
(d) [6] Find .
2. [20] Suppose that, for a particular airline, 25% of all flights are late. The airline randomly selects 50 of their flights. Let X = the number of late flightsamong those selected.
(a) [4] Find .
(b) [4] Find the standard deviation of X.
(c) [8] Use a normal approximation to find .
(d) [4] Suppose instead that only 4% of all of the airline’s flights are late. Show the appropriate computations for deciding whether or not a normal approximation would be a good method for finding probabilities for X. Is a normal approximation a good method in this case? (Circle one.) Yes No
4. [10] The density for a random variable X is given by
.
Given that , find and .
