The time (in minutes) between arrivals of customers to a post office is to be modelled by the Exponential distribution with mean 0.680.68.

The number of days between precipitation events during the fall season is modeled by an exponential distribution with mean 9.7. Compute the probability that the next inter-arrival time for precipitation events is more than 7 days. Use three decimal place accuracy.

Data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. According to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 1.6 standard deviations below the mean? What is the probability that the percent change in worker output from the previous quarter is between -1.56 and 4.33?

Please use excel formulas when possible:   You have a device that uses a single battery, and you operate this device continuously, never turning it off. Whenever a battery fails, you replace it with a brand new one immediately. Suppose the lifetime of a typical batteryhas an exponential distribution with mean 205 minutes. Suppose you operate the device continuously for three days, making battery changes when necessary. Find the probability that you will observe at least 25 failures. (Hint: The number of failures is Poisson distributed.) In the previous problem, we ran the experiment for a certain number of days and then asked about the number of failures. In this problem, we take a different point of view. Suppose you operate the device, starting with a new battery, until you have observed 25 battery failures. What is the probability that at least 15 of these 25 batteries lived at least 3.5 hours? (Hint: Each lifetime is exponentially distributed