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

Answer:

The coefficient of variation after the tax is imposed is 0.033

Step-by-step explanation:

Given

$\mu =1000$ --- mean

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

$tax = 10\%$

Required

The coefficient of variation

The coefficient of variation is calculated using:

$CV = \frac{\sqrt{\sigma^2}}{\mu}$

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:

$CV = \frac{\sqrt{\sigma^2}}{\mu}$

$CV = \frac{\sqrt{1320}}{1100}$

$CV = \frac{36.33}{1100}$

$CV = 0.033$