Statistics 101 Problem Set #5 Fall 1999

 Exercise 5.48 Page 217
 Exercise 5.49 Page 217

 Exercise 5.56 Page 223
 Exercise 5.57 Page 224
 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:
 The probability, P, that the project will be done in less than one year.
 The time, T, such that there is only a 10% chance that the project will take more than T months.
 Find P and T assuming that Y is uniformly distributed with the above mean and
standard deviation.
 Find P and T assuming that Y is exponentially distributed with the above mean.

Find P and T assuming that Y is normally distributed with the above mean and
standard deviation.
 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.
 Write an expression (do not calculate) for the probability that there will be more than
450 cars on a day between 5 and 6PM.
 Find a suitable approximation to the probability in a).
 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 56PM. Note: You may assume that the
probability is .02 that there will be fewer than 360 cars during
any evening rush hour.
 What assumption(s) did you make in answering c)? Are the
assumptions reasonable?
 Find an approximation to the probability in c) using the Poisson
distribution.
 Find an approximation to the probability in c) using the Normal
distribution.

 Exercise 6.31 Page 255
 Exercise 6.32 Page 256
 Exercise 6.33 Page 256
 Exercise 6.34 Page 256

 Exercise 6.44 Page 257
 Exercise 6.45 Page 257