1. Mike and Susan recently won a late-model sports car in a sweepstakes drawing. Not wanting the car for themselves, they decided to sell it. An internet “car lot” shows 20 recent sales of similar cars, with the following final selling prices:
4050, 3750, 3100, 4540, 1800, 4400, 3995, 3670, 3900, 5000, 3730, 4130, 4005, 2100, 4120, 4200, 4540, 3775, 3700, 4180
a) Suppose Mike and Susan want a quick sale. What should their approximate price be if they are willing to let their car go at approximately the 10th percentile?
b) Now suppose Mike and Susan would like their car’s sale price to reflect the central tendency of the population of similar cars that are sold. Is there anything exhibited by these data that might make the median preferable to the mean with respect to setting a final sale price?
2. A new medicine has an 85% success rate. Twenty patients are treated with it. What is the probability that the number of patients cured will be between 7 and 12, both inclusive?
3. Output from a laminating process is acceptable so long as the lamination is at least 8 nm thick but not more than 12 nm thick. The lamination process, when operating correctly, has a mean of 10 nm and a standard deviation of 0.8 nm.
a) What percentage of the output from this process will be defective?
b) If the mean of this process shifts to 10.2 nm without the shift being detected, what percentage of the output will be defective?
4. A test on 36 motorboats reveals that the boat runs continuously for 11.2 hours, on the average, on a full tank, with a standard deviation of 2.3 hours. Construct a 95% confidence interval for the mean time the boat runs.
5. After a change in the regulatory climate, a wireless phone service provider is unsure about the population mean for monthly data usage. The firm will invest in additional capacity if it has sufficient evidence (α = 0.10) that the average data usage is more than 525 kilobytes per month. It is assumed that monthly data usage is normally distributed. A random sample of 20 customers is taken, and a sample average of 550 kilobytes and a sample standard deviation of 83.4 kilobytes are observed. Given the acceptable risk of a Type I error, should the firm invest in the additional capacity?