1. Consider the stem-and-leaf diagram of What family of distributions is suggested by the diagram?

2. Liquid products were first obtained from coal in England during the 1700s. Lamp oil was produced from coal in the United States as early as 1850 but the domestic coal chemicals industry did not develop until World War I. A modem coal-for-recovery system uses a battery of coke ovens to produce liquid products from the coal feed. These observations are obtained on the random variable X, the number of gallons of liquid product obtained per ton of coal feed. (Based on a report in McGraw-Hill Yearbook of Science and Technology, 1983, p. 37.)

(a) Construct a stem-and-leaf diagram for these data. Use the numbers 5,6, 7, 8, 9,10 as stems.

(b) Is the assumption that X is normally distributed justifiable? Explain.

(c) Use the method outlined in this section to break these data into seven categories.

(d) Construct a frequency table and a relative frequency histogram for these data. Does the histogram exhibit the bell shape characteristic of a normal density?

(e) Construct a cumulative frequency table and a relative cumulative frequency ogive for these data. Use the ogive to approximate the probability that a randomly selected ton of coal will yield less than seven gallons of liquid product.