Travel Allowances A survey of local companies found that the mean amount of travel allowance for couriers was $0.25 per mile. The standard deviation was $0.02. Using Chebyshev’s theorem, find the minimum percentage of the data values that will fall between $0.20 and $0.30.

Question

Travel Allowances

A survey of local companies found that the mean amount of travel allowance for couriers was $0.25 per mile. The standard deviation was $0.02. Using Chebyshev’s theorem, find the minimum percentage of the data values that will fall between $0.20 and $0.30.

Accepted Answer

Step 1 Subtract the mean from the larger value.

[latex]\$ 0.30-\$ 0.25=\$ 0.05[/latex]

Step 2 Divide the difference by the standard deviation to get k.

[latex]k=\frac{0.05}{0.02}=2.5[/latex]

Step 3 Use Chebyshev's theorem to find the percentage.

[latex]1-\frac{1}{k^2}=1-\frac{1}{2.5^2}=1-\frac{1}{6.25}=1-0.16=0.84 \quad ext { or } \quad 84 \%[/latex]

Hence, at least 84 % of the data values will fall between $0.20 and $0.30.

Chapter 3

Q. 3.26

Q. 3.26

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