**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 strikes*during 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.)

A. Poisson | B. Uniform | C. Binomial | D. Exponential | E. Normal |

(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 flights*among 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

.