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Chapter 4: Q91E (page 262)
Suppose the random variable x is best described by a normal distribution with and . Find the z-score that corresponds to each of the following x values:
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Errors in measuring truck weights. To help highway planners anticipate the need for road repairs and design futureconstruction projects, data are collected on the estimatedvolume and weight of truck traffic on specific roadways (Transportation Planning Handbook, 2016) using specialized 鈥渨eigh-in-motion鈥� equipment. In an experiment involving repeated weighing of a 27,907-pound truck, it wasfound that the weights recorded by the weigh-in-motionequipment were approximately normally distributed witha mean of 27,315 and a standard deviation of 628 pounds
(Minnesota Department of Transportation). It follows thatthe difference between the actual weight and recordedweight, the error of measurement, is normally distributedwith a mean of 592 pounds and a standard deviation of 628pounds.
a. What is the probability that the weigh-in-motion equipment understates the actual weight of the truck?
b. If a 27,907-pound truck was driven over the weigh-in-motion equipment 100 times, approximately howmany times would the equipment overstate the truck鈥檚weight?
c. What is the probability that the error in the weightrecorded by the weigh-in-motion equipment for a27,907-pound truck exceeds 400 pounds?
d. It is possible to adjust (or calibrate) the weigh-in-motion equipment to control the mean error of measurement. At what level should the mean error beset so the equipment will understate the weight of a27,907-pound truck 50% of the time? Only 40% of thetime
Ages of 鈥渄ot-com鈥� employees. The age (in years) distribution for the employees of a highly successful 鈥渄ot-com鈥� company headquartered in Atlanta is shown in the next table. An employee is to be randomly selected from this population.
Types of finance random variables. Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. The following variables are of interest to security analysts. Which are discrete and which are continuous random variables?
a. The closing price of a particular stock on the New York Stock Exchange.
b. The number of shares of a particular stock that are traded each business day.
c. The quarterly earnings of a particular firm.
d. The percentage change in earnings between last year and this year for a particular firm.
e. The number of new products introduced per year by a firm.
f. The time until a pharmaceutical company gains approval from the U.S. Food and Drug Administration to market a new drug.
Gender discrimination suit. The Journal of Business & Economic Statistics (July 2000) presented a case in which a charge of gender discrimination was filed against the U.S. Postal Service. At the time, there were 302 U.S. Postal Service employees (229 men and 73 women) who applied for promotion. Of the 72 employees who were awarded promotion, 5 were female. Make an inference about whether or not females at the U.S. Postal Service were promoted fairly.
If x is a binomial random variable, compute for each of the following cases:
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