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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.) 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 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 .

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.)

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 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

  .

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