To find the mean of a set of numbers, we need to add all the numbers in the set and then divide the sum by the number of numbers in the set. In this case, the sum of the numbers is 15p, and since there are 5 numbers in the set, the mean is 15p/5. We are given that the mean is 6, so we can set up the following equation:

15p/5 = 6

Solving for p, we get p = 2.

Once we know the value of p, we can calculate the standard deviation of the set of numbers. To do this, we need to first calculate the difference between each number and the mean, square each difference, and then average the squared differences.

The numbers in the set are 2, 4, 6, 8, and 10, and their mean is 6, so the differences between each number and the mean are -4, -2, 0, 2, and 4. Squaring each difference, we get 16, 4, 0, 4, and 16. Averaging these squared differences, we get 10.

Finally, to find the standard deviation, we need to take the square root of the average squared difference. The square root of 10 is approximately 3.16227766, so the standard deviation of the set of numbers is approximately 3.16227766.