Question: 30 Contracts

Thirty closed-out contracts are selected at random to determine the performance of each. The results are expressed in percent profit (a negative value indicates a loss) as follows:

15.2 7.2 0.1 10.9 2.5

14.1 4.8 -2.8 7.4 12.5

8.3 9.1 10.2 5.1 -4.2

6.0 13.2 3.8 18.1 5.5

11.5 3.9 4.2 3.1 -0.5

11.9 6.7 16.5 9.5 1.9

(a) Describe these data in terms of the sample mean, median, range, variance, and standard deviation and graphical techniques including time series, Box Plot, stem-and-leaf plot, histogram, and relative frequency distribution.

(b) Select an appropriate probability distribution using probability plotting as a basis for your selection.

(c) If the percent profit has a normal probability distribution,

i) Estimate the population mean and standard deviation profit margin in terms of point estimates and 90% confidence intervals.

ii) Estimate the probability that a contract will result in a loss. Assess the possible error in your estimate in terms of a 90% confidence interval.