Chapter 7.5, Problem 32E

To determine

To state: The reason why integration gives a good estimate for the probability, even in the discrete case. The discrete probabilities determine rectangles above the individual test scores, so that there actually is a nonzero probability of scoring, say 560. The rectangles would look like the figure below, and would have total area 1.

  

Answer to Problem 32E

Integration is considered a good approximation to the area which represents the probability because the area is a kind of sum.

Explanation of Solution

Given information:

The given figure is shown below:

  

Probabilities are of two types: Continuous and Discrete

A discrete probability includes all the possible values of the random variables, with its probability.

The discrete probabilities determine rectangles above the individual test scores, so that there actually is a nonzero probability of scoring, say 560. The rectangles would look like the figure below, and would have total area 1.

  

Integration is considered as a good approximation to the area which represents the probability.

Since the area is a kind of sum.