Linear transformations: Taxes and fees Assume prices for used Audi A4s available on carmax.com follow a normal distribution with mean $23,800 and standard deviation $4,380.

a. Prices quoted on carmax.com are without sales tax.

To account for a 6% sales tax, you multiply each price by 1.06. What is the distribution of these new prices that include tax? (Hint: When multiplying values of a random variable by a constant [such as multiplying all prices by 1.06], the mean and the standard deviation of this new random variable are simply the mean and the standard deviation of the original variable multiplied by that same constant. The shape of the distribution is not affected by multiplying.)

b. Carmax.com adds a $199 processing fee when a vehicle is sold through its Web page. What is the distribution of the prices when this fee is added to all prices? (Hint:

When adding a constant to values of a random variable

[such as adding 199 to all prices], the mean of this new random variable is obtained by simply adding the same constant to the original mean. The standard deviation, however, is unaffected by the addition, so the standard deviation of the new variable is the same as the standard deviation of the old variable, regardless of how much is added [or subtracted]. The shape of the distribution is also not affected by adding a constant to all values.)