"quantity"exercise: Chebyshev’s inequality
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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
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).
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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