an archer shoots arrows at the bull's eye of a target and measures the distance from the center of the target to the arrow. identify the random variable of interest, determine whether it is discrete or continuous, and list its possible values
since the variable of interest is distance, it is continuous.
Unless you are measuring the number of shots, which is discrete, but might be involved in a different sampling scheme...
The random variable of interest in this scenario is the distance from the center of the target to the arrow. This random variable can be considered continuous since it can take on any real value within a certain range. The possible values for this random variable depend on the size of the target but can include any positive real number greater than or equal to zero.
The random variable of interest in this scenario is the distance from the center of the target to the arrow. Let's determine whether it is discrete or continuous first.
If the measurement can take on any value within a range, then it is a continuous random variable. On the other hand, if the measurement can only take on certain specific values, then it is a discrete random variable.
In this case, the measurement of distance can technically take on any value within a certain range due to the continuous nature of space. However, in practical terms, when measuring the distance from the center of the target to the arrow, there is a limit to the precision of the measurement. Due to the limitations of measurement devices and human ability, the measurement can only be made up to a certain level of precision, resulting in a discrete random variable.
The possible values of this discrete random variable would depend on the level of precision of the measurement device. Let's say, for example, that the measurement device used can measure distances up to the nearest millimeter. In that case, the possible values of the random variable would be integers representing millimeters. If we assume a maximum radius of the target of 100 centimeters, then the possible values of the random variable would be integers from 0 to 1000, representing distances in millimeters from the center of the target to the arrow.