A random sample of data has a mean of 65 and a variance of 36 a. Use Chebychev\'

Question

A random sample of data has a mean of 65 and a variance of 36 a. Use Chebychev's theorem to determine the percent of observations between 53 and 77. b. If the data are mounded, use the empirical rule to find the approximate percent of observations between 53 and 77. a. Using Chebychev's theorem, the portion of the data which are between 53 and 77 is at least (Round to one decimal place as needed.) 9 %. b. Using the empirical rule, approximately 1% of the data are between 53 and 77. (Round to the nearest whole number as needed.)

Explanation / Answer

ANSWER:

A) x1 = 53 and x2 = 77

mean = 65 and variance = 36 and std = (variance) ^ 1 / 2 = (36) ^ 1 / 2 = 6

(x1 - mean) / std = ( 53 - 65 ) / 6 = -12 / 6 = -2 std to the left of mean

(x2 - mean) / std = ( 77 - 65 ) / 6 = 12 / 6 = 2 std to the right of mean

chebychev says at least (1 - (1 / k ) ^ 2 ) lies in interval that is ( 1 - ( 1 / 2) ^ 2) = ( 1 - 1 / 4) = 3 / 4 = 75%

b) approximately 95%of the data is in the interval.

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