Question

Describe a practical problem or article that uses a probability distribution studied in these chapters. You can find an example from business, a scientific study or your own experience. Write a brief report describing this study and the practical value of the solution.

Answer 1

Example of discrete case: Suppose we are interested in

determining the number of heads obtained in 10 tosses of

a coin. Let X be the random variable denoting the number of

heads obtained in 10 tosses. If we assume the coin to be

fair i.e. the probability obtaining the head is almost same as

obtaining a tail. So we can assume the probability to be 0.5.

Hence, X ~ Bin (10, 0.5).

Continuous case: Suppose we are interested in observing the

performance of the students of a class in a particular test.

Suppose the number of students in the class is 120.

The average score of a test is 70 out of 100 and the variance

is 25. Moreover, assume the distribution of the scores is

bell-shaped. Thus, we can assume the distribution of scores

to be Normal i.e. N(70, 25).