The semi-logarithmic scale is so named because:
Answer(s): D
Values on the y-axis are equally spaced if there are equal differences in their logarithms. Thus, 100 is as close to 10, as 10 is to 1. (In base 10, log 100 - log 10 = 1, log 10 - log 1 = 1; in base e, the differences are also the same, each equal to 2.302.)
The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?
Answer(s): A
z = (x - u)/sigma. z1 = (32000 - 40000)/5000 = -1.6. z2 = (42000 - 40000)/5000 = 0.4. The area under the curve for the respective z values are 0.4452 and 0.1554. Since the earnings are on the opposite sides of the mean, we add them up 0.4452 + 0.1554 = 0.6006.
The weights of cans of fruit are normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What portion of the cans weigh 860 grams or less?
Answer(s): E
z = (x-u)/sigma = 860 - 1000/50 = -2.8. For z = 2.8, the area is 0.4974. So 1.0 - 0.9974 = 0.0026.
You are examining the return on equity ratios of the nation's commercial airlines. You have calculated the mean ROE to be 8%, and the sum of the squared ROEs is 0.27. Assuming there are 30 commercial airlines, what is the population standard deviation of ROEs in this industry?
The population standard deviation is the positive square root of the population variance. The population variance is equal to the sum of the squared differences between each population member and the population mean, divided by the number of items in the population. There is, however, an equivalent alternate formula that is more often used for large amounts of calculation. It is equal to the average squared observation less the squared mean. In this case, we have the average squared observation will be 0.27 / 30 = 0.009, less the squared mean of 8%. We have 0.009 - 0.0064 = 0.0026 = 26%%. The square root of this number, 5.1%, will be the population standard deviation.
The U.S. Department of Education reported that for the past seven years 4,033, 5,652, 6,407, 7,201, 8,719, 11,154, and 15,121 people received bachelor's degrees in computer and information sciences. What is the mean annual number receiving this degree?
Answer(s): C
(4033 + 5652 + 6407 + 7201 + 8719 + 11154 + 15121)/7 = 8327
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