many states have a pick 3 lottery in which three digits are

many states have a pick 3 lottery in which three digits are randomly selected each day. winning requires that you select the same three digits in the same order that they are drawn. assume that you compute the mean of each set of three selected digits.

a. what is the approximate shape of the distribution?

b. what value do the sample means target? that is, what is the mean of all such sample means?

c. for each set of 3 digitd that is selected, if you find the proportion of odd numers, what is the mean of those proportions?

Solution

a)

It is approximately normal (bell shaped), by the central limit theorem.

b)

As digits are drawn from 0 to 9.Thus, the mean value of a digit is (0+9)/2 = 4.5.

Thus, the mean of the sample means must be 4.5. [ANSWER]

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c)

As half of the digits are odd numbers, then the mean of those proportions must be 0.5. [ANSWER]