Chapter 3

Q. 3.26

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.


Verified Solution

Step 1 Subtract the mean from the larger value.

\$ 0.30-\$ 0.25=\$ 0.05

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


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

1-\frac{1}{k^2}=1-\frac{1}{2.5^2}=1-\frac{1}{6.25}=1-0.16=0.84 \quad \text { or } \quad 84 \%

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