2-40 Armstrong Faber produces a standard number-two pencil called Ultra-Lite. Si

Question

2-40 Armstrong Faber produces a standard number-two pencil called Ultra-Lite. Since Chuck Armstrong started Armstrong Faber, sales have grown steadily. With the increase in the price of wood products, however, Chuck has been forced to increase the price of the Ultra-Lite pencils. As a result, the demand for Ultra-Lite has been fairly stable over DISCUSSION QUESTIONS AND PROBLEMS 63 the past 6 years. On the average, Armstrong Faber has sold 457,000 pencils each year. Furthermore, 90% of the time sales have been between 454,000 and 460,000 pencils. It is expected that the sales follow a normal distribution with a mean of 457,000 pencils. Estimate the standard deviation of this distribution. (Hint: Work backward from the normal table to find Z. Then apply Equation 2-15.)

2-15 A silver dollar is flipped twice. Calculate the probability of each of the following occurring: (a) a head on the first flip (b) a tail on the second flip given that the first toss was a head (c) two tails (d) a tail on the first and a head on the second (e) a tail on the first and a head on the second or a head on the first and a tail on the second (f) at least one head on the two flips

Explanation / Answer

2-40.

90% of values are between 454000 and 460000, which are symmetric about the mean of 457000.

Hence for the middle 90%, the area of each outer tail is (1-0.90)/2 = 0.05. Hence, the z score for that is, by table,

z = 1.645

Hence, for x = 460000

sigma = (x-u)/z = (460000-457000)/1.645 = 1823.71 [ANSWER]

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