1. A search aircraft is searching for a smuggler’s diesel submarine on a known route from South America to the US.Based on prior information about smugglers’ habits we expect the submarine to expose its periscope about every half hour to collect electronic and visual information.

a. Given the search aircraft can illuminate a certain operating area with its radar (radar flood) for 45 minutes, what are the chances (assuming this is a Poisson process ) our radar operator will have more than one opportunity to “catch” the periscope raised?Give answer to two decimals places.

b. With 20 minutes left on station, our radar operator just saw a periscope sink moments ago.Assuming the submarine is not aware of our presence, what are the chances that the aircraft will have another opportunity to see the periscope before returning to base?Give answer to two decimals places.

2. Two types of UAVs were launched off of USN ships during a recent deployment.Two out of every three UAVs were made by Manufacturer A and the rest were made by Manufacturer B.If 117 sequential launches were conducted during the deployment with no UAVs lost and the UAV for the next upcoming launch was chosen at random, then what is the approximate probability that at most 72 of these launched UAVs were made by Manufacturer A?Show all work.

3. In an effort to make a leaner Army, the new ground assault vehicle is said, by the manufacturer, to attain 25 miles per gallon on the test range.You doubt the claim and ask for their data.A contractor working on this vehicle provides you with a list of eight test vehicles that together had a mean of 23 miles per gallon and a sample standard deviation of 5 miles per gallon (s = 5).Write an appropriate null and alternative hypothesis, find the test statistic, find the p-value (or give a range), and provide a brief analysis of your findings.Show all work.Include in your analysis your thoughts on the objectivity of the data provided.

4. The mean time to complete work ups for 13 randomly selected aircrew at Squadron A is 230.9 hours with a sample standard deviation of 1.3 hours (s = 1.3) and the mean time to complete work ups for 15 randomly selected aircrew at Squadron B is 227.9 hours with a sample standard deviation of 1.1 hours (s = 1.1).The commander of Squadron A tells the wing this is sufficient evidence to conclude there is no difference in work up time between the two squadrons.Assuming the populations are normally distributed and the variances are equal use the given information to make a case to support or refute the commander’s claim.Show all work

5. In how many ways can six watch-standers be assigned to five different stations on a ship with at least one watch-stander at each station.Since there are six watch-standers to assign, there will be two watchstanders assigned to one of the five stations.Show all work.