Question

How do you work out this problem?

The answer I was given is choice B.

1) A sample of 68 books has a mean cost of $ 70.27 and a standard deviation of $ 7.83. Use this information and the special cases of Chebychev's rule to complete the statements below: and (i) At least 51 of the 68 books cost between (ii) At least of the 68 books cost between $ 46.78 and $ 93.76. A) (i) $50.70, $ 89.85 (ii) 56 C) (i) $62.44, $ 78.10 (ii) 61 B) (i) $54.61, $ 85.93 (ii) 61 D) (0) $ 46.78, $ 93.76 (ii) 52

Answer 1

Answer)

According to the chebyshev's theorem

At least 1 - (1/k^2) lies with in k standard deviation

1)

51/68 = 0.75 = 75%

1 - (1/2^2) = 75%

So k = 2

Answer is 70.27 - (2*7.83) and 70.27 + (2*7.83)

Between 54.61 and 85.93

2)

46.78 = mean - (3*s.d)

93.76 = mean + (3*s.d)

So k = 3

Answer is 1 - (1/3^2) = 89%

89% of 68 = 61