Final answer:
The life x of a battery in constant use is typically modeled using an A. exponential distribution. This distribution is suitable for representing the time until an event, like a battery failing, occurs.
Step-by-step explanation:
The life x (in hours) of a battery in constant use is most likely to follow an exponential distribution. This is because the exponential distribution is often used to model the time until a specific event occurs, such as the failure of a battery. When we say that a car battery life decays with a parameter of 0.025, we are implying that the time until the battery no longer functions is exponentially distributed with a rate parameter of 0.025. This means that as time goes on, the probability of the battery failing in the next instant, given that it has not failed yet, remains constant. When plotted on a logarithmic scale, an exponential decay appears as a straight line.
In the context of random variables, X can be defined as the random variable representing the life of the car battery in months, and X is indeed continuous. In this case, the continuous nature of the variable X allows us to handle a range of values without breaks or gaps.
In a practical scenario like investigating the company's claim about the average life span of batteries, statistical methods such as hypothesis testing using the sample mean would be applied. If the sample mean is significantly lower than the claimed mean, this could raise doubts about the claim's validity.