Question

The cost of a week long vacation in a city has a mean of 1000 and a variance of 1200. The city imposes a tax which will raise all tourism related costs by 10%. Find the coefficient of variation for the cost of a week long vacation in this city after the tax is imposed.

Answer 1

The coefficient of variation after the tax is imposed is 0.033

Explanation:

Given

`\mu =1000` --- mean

`\sigma^2 = 1200` --- variance

`tax = 10\%`

Required

The coefficient of variation

The coefficient of variation is calculated using:

`CV = (√(\sigma^2))/(\mu)`

After the tax, the new mean is:

`\mu_(new) = \mu * (1 + tax)`

`\mu_(new) = 1000 * (1 + 10\%)`

`\mu_(new) = 1100`

And the new variance is:

`\sigma^2_(new) = \sigma^2 * (1 + tax)`

`\sigma^2_(new) = 1200 * (1 + 10\%)`

`\sigma^2_(new) = 1320`

So, we have:

`CV = (√(\sigma^2))/(\mu)`

`CV = (√(1320))/(1100)`

`CV = (36.33)/(1100)`

`CV = 0.033`