Based on the following table of hemoglobin levels for miners, compute the probabilities described below. Assume that the proportion in each category for this set of 90 miners is the true proportion for the population of miners.
|
Class Interval for Hemoglobin (g/cc)
|
Number of Miners
|
|
12.0-17.9
|
24
|
|
18.0-21.9
|
53
|
|
22.0-27.9
|
13
|
|
Total
|
90
|
Source: Adapted from Dunn, O. J. (1977). Basic Statistics: A Primer for the Biomedical Sciences, 2nd Edition. Wiley, New York, p. 17.
a. Compute the probability that a miner selected at random from the popula- tion has a hemoglobin level in the 12.0-17.9 range.
b. Compute the probability that a miner selected at random from the popula- tion has a hemoglobin level in the 18.0-21.9 range.
c. Compute the probability that a miner selected at random from the popula- tion has a hemoglobin level in the 22.0-27.9 range.
d. What is the probability that a miner selected at random will have a hemo- globin count at or above 18.0?
e. What is the probability that a miner selected at random will have a hemo- globin count at or below 21.9?
f. If two miners are selected at random from the "infinite population" of min- ers with the distribution for the miners in the table, what is the probability that one miner will fall in the lowest class and the other in the highest (i.e., one has a hemoglobin count in the 12.0 to 17.9 range and the other has a hemoglobin count in the 22.0 to 27.9 range)?