Carol sampled the monthly maintenance costs for automated soldering machines a total of 100 times during 1 year. She clustered the costs into $200 cells, for example, $500 to $700, with cell midpoints of $600, $800, $1000, etc. She indicated the number of times (frequency) each cell value was observed. The costs and frequency data are as follows.

Cell Midpoint, $             Frequency

600 ..............................             6

800 ...........................              10

1000 ..........................               7

1200 ...........................            15

1400 ..........................             28

1600 ...........................            15

1800 ...........................              9

2000 ...........................            10

(a) Estimate the expected value and standard deviation of the maintenance costs the company should anticipate based on Carol’s sample.

(b) What is the best estimate of the percentage of costs that will fall within 2 standard deviations of the mean?

(c) Develop a probability distribution of the monthly maintenance costs from Carol’s sample, and indicate the answers to the previous two questions on it.

(d) Use a spreadsheet to display the sample mean.