单选题

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:

【正确答案】 A
【答案解析】

Calculate and interpret the proportion of observations falling within a specified number of standard deviations of the mean using Chebyshev’s inequality.
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. 382 – (3 × 14) = 340; 382 + 3 × 14 =424.