Final answer:
The mean of the distribution is 22.0000
Step-by-step explanation:
The mean of a distribution can be calculated by adding up all the values in the distribution and dividing by the total number of values. In this case, the random number generator picks a number from 8 to 36 in a uniform manner. Therefore, the mean can be calculated by finding the sum of all the numbers from 8 to 36 and dividing by the total number of values, which is 29.
To find the sum of all the numbers from 8 to 36, you can use the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get Sn = (29/2)(8 + 36) = (29/2)(44) = 638.