| Ch. 2 Exercise 18 | ||||||||
| Ecommerce.com, a large Internet retailer, is studying the lead time (elapsed time between when an order is placed and when it is filled) for a sample of recent orders. The lead times are reported in days. |
||||||||
| Electricity | Cost Frequency | Middle | x-16.45 | |||||
| 0 up to 5 | 6 | 3 | -13.45 | 180.9025 | 1085.415 | -1067.42 | ||
| 5 up to 10 | 7 | 7.5 | -8.95 | 80.1025 | 560.7175 | -508.218 | ||
| 10 up to 15 | 12 | 12.5 | -3.95 | 15.6025 | 187.23 | -37.23 | ||
| 15 up to 20 | 8 | 17.5 | 1.05 | 1.1025 | 8.82 | 131.18 | ||
| 20 up to 25 | 7 | 22.5 | 6.05 | 36.6025 | 256.2175 | -98.7175 | ||
| Total | 40 | 63 | -19.25 | 314.3125 | 2098.4 | -1580.4 | ||
| -39.51 | ||||||||
| a. How Many orders studied. | 40 | 6.285698 | ||||||
| mean = [6*3+7*7.5+12*12.5+8*17.5+8*17.5+7*22.5)/(sum of the freqs) = 16.45 |
||||||||
| mean = | 16.45 | |||||||
| 12.95 | ||||||||
| b. What is the Midpoint of the first class (Round your answer to 1 decimal place.) |
||||||||
| c. What are the coordinates of the first class for a frequency polygon assuming we draw a frequency polygon using the midpoints? (Round your answer to 1 decimal place.) |
||||||||
| x = | ||||||||
| y = | 6.29 | |||||||
| Variance = [ 6(3-12.95)^2 + 7(7.5-12.95)^2 + 12(12.5-12.95)^2 + 8(17.5-12.95)^2 +7(22.5-12.95)^2 ] / 40 = |
||||||||
| = | 40.21 | |||||||
| Square root | 6.341136 | |||||||
| c. Use the Empirical Rule to estimate the proportion of costs within two standard deviations |
||||||||
| of the mean. What are these limits? |
||||||||
| Lower = | -63.97 | |||||||
| Upper = | 56.66 | |||||||
