If 2 is added to each of the 15 numbers with a mean of 30, the new mean becomes 4.
The mean of a set of numbers is the sum of all the numbers divided by the total count of numbers. In this case, the mean of the original 15 numbers is 30. Let's denote the original numbers as x1, x2, ..., x15.
Mean = (x1 + x2 + ... + x15) / 15 = 30
Now, if 2 is added to each number, the new numbers become (x1 + 2), (x2 + 2), ..., (x15 + 2). The new mean can be calculated as follows:
New Mean = [(x1 + 2) + (x2 + 2) + ... + (x15 + 2)] / 15
Simplifying this expression, we get:
New Mean = [(x1 + x2 + ... + x15) + 2*15] / 15
Since the original mean is 30, the expression becomes:
New Mean = (30 + 2*15) / 15
New Mean = (30 + 30) / 15
New Mean = 60 / 15
New Mean = 4
Therefore, if 2 is added to each number, the new mean of the 15 numbers will be 4. The addition of a constant to each number does not affect the mean; it simply shifts the entire distribution by that constant.