Quizzol

QUESTION:

The number of people in a car that crosses a certain bridge is represented by the random variable X, which has a mean value μX = 2.7, and a variance σ2X = 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:

mean = $1.35, variance = $ .30.

mean = $8.60, variance = $ .30.

mean = $8.60, variance = $ .60.

mean = $4.35, variance = $3.30.

mean = $4.35, variance = $ .30.

ANSWER:

mean = $4.35, variance = $ .30.

Good job! Let T be the total amount of money that is collected from a car that crosses the bridge. T is composed of two parts: the fixed toll of 3 dollars (regardless of the number of passengers) and $ .50 for every passenger, thus T = 3 + 0.50 * X. To find the mean and variance of T you need to use the rules of means and variances: Formula for probability with random variables.

Formula for probability with random variables.

Posted by Cleveland on September 22, 2024