This exercise can be done individually or better yet as a class project.

a. Use a table of random numbers or a random-number generator to obtain \(50\) random integers between \(0\) and \(9\).

b. Without graphing the distributions of the \(50\) numbers you obtained, guess its specific shape. Explain your reasoning.

c. Construct a relative-frequency histogram based on single value grouping for the \(50\) numbers that you obtained in part (a). Is its shape about what you expected?

d. If your answer to part (c) was "No" provide an explanation.

e. What would you do to make getting a "yes" answer to part (c) more plausible?

f. If you are doing this exercise as a class project, repeat part (a)-(c) for \(1000\) random integers.

Using random variable table, the \(50\) numbers will be,

(9,0,4,8,8,9,4,5,5,0,6,9,5,4,4,6,9,5,5,0,1,3,9,6,6,5,3,9,5,7,0,8,7,0,4,0,6,0,4,7,7,7,7,2,7,8,8,7,1,1\)

The distribution would be expected to be uniform, because every digit is equally likely and thus it is expected each digit to occur the same number of times.

The frequency distribution is shown below,

The relative frequency histogram is shown below,

The diagram does not appear to be roughly uniform. So, the guess was not correct.

The sample represents only a part of the population and thus we expect sample distribution to resemble the population distribution. There is always a source of sample variability that causes the sample distribution to vary from population distribution.

If the sample taken was large enough to represent the population then answer would be yes.

Repeat part (a) to (c) for \(1000\) random variables instead of \(50\),