Question

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 modern coal - for - recovery system uses a battery of coke ovens to produce liquid products from coal feed. These observations are obtained on the random variable X, the number of gallons of liquid product obtained per coal feed: (insert data)

7.6 8.2 7.1 10.0 6.5 9.6
6.1 6.2 7.6 6.2 9.5 6.7
7.4 9.5 9.2 8.0 8.5 9.3
8.8 9.6 9.7 6.8 7.1 7.7
8.7 7.8 8.7 8.2 8.2 7.4
9.0 8.8 7.3 7.9 7.1 7.9
7.6 6.7 8.1 6.2 5.3 7.4
7.7 9.1 7.9 8.7 8.4 8.1
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). Break these data into six categories
d). Construct a frequency table and relative frequency histogram for these data. Does the histogram exhibit the bell – shape characteristics of a normal density?
e). Construct a cumulative frequency table and relative cumulative frequency ogive for these data. Use the ogive to approximate the probability that a randomly selected ton of coal will yield les than 7 gallons of liquid product.

Answer 1

b) The data is bell shaped hence the assumption of X been normally distributed is correct

c) The categories are

< 5, 5-6, 6-7, 7-8, 8-9, 9-10

d) attached below

e) The probability of < 7 gallons = 0.167

Explanation:

a) stem and leaf diagram for these data

stem leaf

5 .3

6 .1, .2, .2, .2, .5, .7, .7, .8

7 .1, .1, .1, .3, .4, .4, .4, .6, .6, .6, .7, .7, .8, .9, .9, .9

8 .0, .1, .1, .2, .2, .2, .4, .5, .7, .7, .7, .8, .8

9 .0, .1, .2, .3, .5, .5, .6, .6, .7

10 0

b) The data is bell shaped hence the assumption of X been normally distributed is correct

c) The categories are

< 5, 5-6, 6-7, 7-8, 8-9, 9-10

d) attached below

e) The probability of < 7 gallons = 0.167