Question

The number of accidents in a week is ___________?a continuous random variable.a discrete random variable.neither continuous nor discrete variable.continuous and discrete variables.

Answer 1

The number of accidents in a week is a discrete random variable, which is countable and fits into a Poisson distribution if the accidents occur at a consistent average rate. Calculating specific probabilities regarding accidents would require using appropriate probability functions.

Step-by-step explanation:

The number of accidents in a week is a discrete random variable. Discrete random variables are countable, and since we can count the number of accidents, it falls into this category. For example, if we let X represent the number of automobile accidents in a small city, we can use a Poisson distribution to model this discrete random variable, especially if these accidents occur at a consistent average rate per time period.

To calculate the probability that at most two accidents occur in any given week, we would calculate P(X ≤ 2) using the appropriate Poisson probability function. Conversely, determining the probability that there are at least two weeks between any two accidents would require a different approach, possibly involving geometric or exponential distributions depending on how the problem is defined.

Understanding whether data is quantitative discrete or quantitative continuous is critical in selecting the right statistical models and methods for analysis. In the context of accidents per week, since the number is countable, it is definitely a quantitative discrete variable.

Answer 2

a discrete random variable.

Discrete variables are countable in a finite amount of time

Continuous variables would take forever to count. Hopefully we do not have that many accidents. Continuous variables would be like time.

Discrete things are things we can count and thats it, like the amount of change in your pocket, or the number of tic tacs in the container.