Suppose that the useful life of a particular car battery, measured in months, decays with parameter 0.025. We are interested in the life of the battery. Find the probability that a car battery lasts more than 36 months.

The probability that a car battery lasts more than 36 months is 0.4066.

Step-by-step explanation:

Let X = the useful life of a particular car battery.

The decay parameter is, λ = 0.025.

The random variable X follows an Exponential distribution with parameter λ = 0.025.

The probability density function of X is:

Compute the probability that a car battery lasts more than 36 months as follows:

Thus, the probability that a car battery lasts more than 36 months is 0.4066.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2