Studies conducted by a manufacturer of Boston and Vermont asphalt shingles have shown product weight to be a major factor in customers’ perception of quality. Moreover, the weight represents the amount of raw materials being used and is therefore very important to the company from a cost standpoint. The last stage of the assembly line packages the shingles before the packages are placed on wooden pallets. The variable of interest is the weight in pounds of the pallet, which for most brands holds 16 squares of shingles. The company expects pallets of its Boston brand-name shingles to weigh at least 3,050 pounds but less than 3,260 pounds.

For the company’s Vermont brand-name shingles, pallets should weigh at least 3,600 pounds but less than 3,800. Data, collected from a sample of 368 pallets of Boston shingles and 330 pallets of Vermont shingles, are stored in Pallet.

a. For the Boston shingles, construct a frequency distribution and a percentage distribution having eight class intervals, using 3,015, 3,050, 3,085, 3,120, 3,155, 3,190, 3,225, 3,260, and 3,295 as the class boundaries.

b. For the Vermont shingles, construct a frequency distribution and a percentage distribution having seven class intervals, using 3,550, 3,600, 3,650, 3,700, 3,750, 3,800, 3,850, and 3,900 as the class boundaries.

c. Construct percentage histograms for the Boston and Vermont shingles.

d. Comment on the distribution of pallet weights for the Boston and Vermont shingles. Be sure to identify the percentages of pallets that are underweight and overweight.