The number of people in a car that crosses a certain bridge is represented by the random variable x, which has a mean value = 2.7, and a variance = 1.2. the toll on the bridge is $3.00 per car plus $ .50 per person in the car. the mean and variance of the total amount of money that is collected from a car that crosses the bridge are: a. mean = $1.35, variance = $ .30.b. mean = $8.60, variance = $ .30.c. mean = $8.60, variance = $ .60.d. mean = $4.35, variance = $3.30.e. mean = $4.35, variance = $ .30.

And then we have the following parameters for the random variable Y

And the best option is:e. mean = $4.35, variance = $ .30.

Step-by-step explanation:

For this case we know the following info " The toll on the bridge is $3.00 per car plus $ .50 per person in the car"

So then we can create the following linear function:

Where Y represent the total amount of money that is collected from a car. And X represent the number of people in the car.

We have the parameters for the random variable X given by:

So then we can find the expected value for the random variable Y like this:

And if we replace the expected value for X we got this:

Now we can find the variance for the random variable Y like this:

We know that for a number we don't have variance since is a constant and the covariance between a number and a random variable is 0 so then we have just this for the variance of Y:

And then we have the following parameters for the random variable Y

And the best option is:e. mean = $4.35, variance = $ .30.