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For the data in the spreadsheet assessment3.xls, calculate the:
1. mean:
-18.05
-16.49
17.19
59.63
2. median:
-18.05
-16.49
17.19
59.63
3. range:
-18.05
-16.49
17.19
59.63
4. standard deviation:
-18.05
-16.49
17.19
59.63
5. To maximize profits, airlines strive to assign airplanes with the proper capacity to each route, a problem known as the flight assignment problem. If an airplane is too large, the airlines spends more money in fuel flying a larger plane than necessary. If the airplane is too small, business is lost to other airlines when the plane is full. The number of passengers not carried because the airplane is too small is known as spill. In a 1994 article in Interfaces by Subramanian, Scheff, Quillinan, Wiper and Marsten, demonstrate an approach to assigning aircraft to routes at Delta Airlines using an optimization model, assuming that the number of passengers wanting to fly a particular route is normally distributed.
Suppose that the number of passengers desiring to fly from Atlanta to Miami at 10:00 AM is normally distributed with a mean of 184 with a standard deviation of 37. The airline is considering assigning a Boeing 757-300 with 239 seats to the route. If it makes this assignment, what fraction of flights will have spill, i.e., what fraction of flights will turn one or more passengers away?
1.5%
3.4%
6.9%
13.7%
6. A manufacturer of automated test equipment claims that it has a system that can accurately evaluate the surface finish of machined parts with a surface area of less than 5 sq. in. at the rate of 5 per minute. A potential customer agrees to evaluate the tester in its facility, and runs 100 batches of 50 parts, recording the processing time for each batch in the following spreadsheet:
A 95% confidence interval for the number of units the inspector can process in a minute is:
5.38 +/- 0.18
5.38 +/- 0.90
9.54 +/- 0.30
9.54 +/- 1.52
7. In a 1995 article in Psychological Assessment reported on a study comparing the level of post-traumatic stress disorder (PTSD) in WWII aviators who were German prisoners-of-war (POW) with Vietnam war POWS. For Vietnam POWs, the average PTSD score is 16. For a sample of 33 German POW aviators, the average PTSD score was 9.0 with a standard deviation of 9.32. What is the probability that the German POWs have the same level of PTSD as Vietnam POWs given the data in the sample, i.e. what is the p-value?
0.000008
0.0008
0.045
0.226
8. The U.S. Golf Association (USGA) requires that, among other requirements, golf balls weigh between 1.620 and 1.680 ounces avoirdupois . The USGA periodically checks a manufacturers golf balls by testing two dozen golf balls randomly selected from pro shops around the country. If more than 3 of the two dozen golf balls fail the tests, the brand is removed from the USGA approved list.
Suppose a manufacturer has developed a new type of golf ball that easily meets all of the USGA requirements except weight. In their own experiments, the suspect that 10% of all golf balls they produce are outside of the weight specification. If that is the case, what is the probability that they will fail a USGA inspection?
13%
21%
79%
87%
9. Obstructive sleep apnea is a sleeping disorder that occurs when a sleeping person stops breathing momentarily and awakens briefly. This may occur hundreds of times a night, which can reduce the quality of sleep and leave the person fatigued. It is estimated that 25% of the general population suffers from sleep apnea. In a 1995 study in the journal Chest, a random sample of 159 commercial truck drivers was studied and 124 were found to suffer from sleep apnea. What is the probability that the proportion of truck drivers with sleep apnea is no different from that of the general population given the data in the sample, i.e. what is the p-value?
0.001
0.01
0.05
practically zero