"quantity"exercise: Chebyshev’s inequality

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來源: 正保會(huì)計(jì)網(wǎng)校編輯：小鞠橘桔 2020/11/10 14:20:46　字體：大小

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Questions 1:

A sample of 438 observations is randomly selected from a population. The mean of the sample is 382, and the standard deviation is 14. Based on Chebyshev’s inequality, the endpoints of the interval that must contain at least 88.89% of the observations are closest to:

A、 340 and 424.

B 、396 and 480.

C、 354 and 410.

Questions 2:

Compared with the occurrence of fundamental developments related to a company, when do technical analysts believe that related security price movements are most likely to arise?

A、 After

B、 Before

C、 Simultaneously

View answer resolution

【Answer to question 1】A

【analysis】

A is correct. According to Chebyshev’s inequality, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 – 1/k2 for all k >1. For k = 3, that proportion is 1 – 1/32, which is 88.89%. The lower endpoint is, therefore, the mean (382) minus 3 times 14 (the standard deviation), and the upper endpoint is 382 plus 3 times 14 (i.e., 340 and 424, respectively).

C is incorrect; it is based on 2 standard deviations, not 3: 382 – 2 × 14 = 354 and 382 + 2 × 14 = 410. B is incorrect; it centers the interval around the number of observations (438) rather than the mean (382).

【Answer to question 2】B

【analysis】

B is correct. Technicians believe that security price movements occur before fundamental developments of a company unfold and before they are reported to the public.

A is incorrect. Technicians believe that security price movements occur before, not after, fundamental developments unfold—certainly before they are reported.

C is incorrect. Technicians believe that security price movements occur before, not at the same time as, fundamental developments unfold—certainly before they are reported.

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