1. A family of mutual funds maintains a service that allows clients to switch money among accounts through a telephone call. It was estimated that 3.2% of callers that get a busy signal hang up. If this data set can be described as a Bernoulli distribution, find the mean and standard deviation of the number of callers who hang up after getting a busy signal.

1. A campus finance officer finds that, for all parking tickets issued, the probability that the fine will be paid is .78. In the most recent week, 620 parking tickets have been issued.

A. Find the mean and standard deviation of the number of these tickets for which the fines will be paid if this data set can be described as a binomial distribution.

B. Assume that there is a linear relationship between fines paid and the amount of money obtain from fine, and that this relationship can be described by

Z =2X. Use this information to find the mean and standard deviation of the amount of money that will be obtained from the payment of these fines.

3. Customers arrive at a busy checkout counter at an average rate of 3 per minute. If the distribution of arrivals is Poisson, find the probability that in any given minute there will be (a) 0 arrival, (b) 1 arrival, (c) 2 arrivals (d) less than 2 arrivals?

4. The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4 miles long. Experience has shown that the distance along this stretch, measured in miles from its northernmost point, at which an emergency occurs can be represented by a uniformly distributed random variable over the range 0 to 4 miles.

A. Find the probability density function

B. Find the probability that a given emergency that arose is less than 1 mile on this

stretch of river

C. Find the probability that a given emergency that arose is more than 2 miles on this stretch of river.