A sample of 56 books has a mean cost of $91.14 and a standard deviation of $9.02. Use this information and the special cases of Chebychev's rule to complete the statements below:
(i) At least 42 of the 56 books cost between ____and____
(ii) At least ______of the 56 books cost between $\$ 64.08$ and $\$ 118.20$.
A)(i) $\$ 68.59 , \$ 113.69$
(ii) $46$
B) (i) $\$ 82.12 , \$ 100.16$
(ii) $50$
C) (i) $\$ 73.10 , \$ 109.18$
(ii) $50$
D) (i) $\$ 64.08 , \$ 118.20$
(ii) $43$

Question

A sample of 56 books has a mean cost of $91.14 and a standard deviation of $9.02. Use this information and the special cases of Chebychev's rule to complete the statements below: 
(i) At least 42 of the 56 books cost between ____and____
(ii) At least ______of the 56 books cost between $\$ 64.08$ and $\$ 118.20$.  
A)(i) $\$ 68.59 , \$ 113.69$
(ii) $46$
B) (i) $\$ 82.12 , \$ 100.16$
(ii) $50$
C) (i) $\$ 73.10 , \$ 109.18$
(ii) $50$
D) (i) $\$ 64.08 , \$ 118.20$
(ii) $43$

Quizplus · Accepted Answer

Chebyshev's rule states that at least $1 - \frac{1}{k^2}$ of data falls within $k$ standard deviations from the mean. For (i), using $k=2$, at least 75% (42 books) fall within 2 standard deviations: $91.14 \pm 2(9.02)$. For (ii), using $k=3$, at least 88.89% (50 books) fall within 3 standard deviations: $91.14 \pm 3(9.02)$.

A Sample of 56 Books Has a Mean Cost of $91.14