## Statistics 101 Problem Set #5 Fall 1999

1. Exercise 5.48 Page 217
2. Exercise 5.49 Page 217

1. Exercise 5.56 Page 223
2. Exercise 5.57 Page 224

1. The time it takes to complete a project, Y, has a mean of 16 months and a standard deviation of 4 months. The following two quantities are of interest:

1. The probability, P, that the project will be done in less than one year.
2. The time, T, such that there is only a 10% chance that the project will take more than T months.

1. Find P and T assuming that Y is uniformly distributed with the above mean and standard deviation.
2. Find P and T assuming that Y is exponentially distributed with the above mean.
3. Find P and T assuming that Y is normally distributed with the above mean and standard deviation.

2. The number of cars that arrive at the toll booths on the Benjamin Franklin Bridge during evening rush hour (i.e., between 5 and 6PM) has a Poisson distribution with mean of 400 cars.

1. Write an expression (do not calculate) for the probability that there will be more than 450 cars on a day between 5 and 6PM.
2. Find a suitable approximation to the probability in a).
3. Write an expression (do not calculate) for the probability that there will be more than 10 days in a year (260 weekdays) with fewer than 360 cars during 5-6PM. Note: You may assume that the probability is .02 that there will be fewer than 360 cars during any evening rush hour.
4. What assumption(s) did you make in answering c)? Are the assumptions reasonable?
5. Find an approximation to the probability in c) using the Poisson distribution.
6. Find an approximation to the probability in c) using the Normal distribution.
1. Exercise 6.31 Page 255
2. Exercise 6.32 Page 256
3. Exercise 6.33 Page 256
4. Exercise 6.34 Page 256
1. Exercise 6.44 Page 257
2. Exercise 6.45 Page 257