Final answer:
Option D. To find the new mean of a set when an additional number is added, sum all the numbers, including the new one, and then divide by the new total count of numbers in the set. The correct new mean for the given set with 40 added is 38.
Step-by-step explanation:
To find the new mean, you need to add 40 to each number in the set first. So the new set of numbers becomes {72, 56, 96, 80, 64, 85, 51}. Next, add up all the numbers in the set: 72 + 56 + 96 + 80 + 64 + 85 + 51 = 504. Since there are 7 numbers in the set, divide the sum by 7 to find the mean: 504 ÷ 7 = 72. Therefore, the new mean of the set of numbers is 72.
The question is asking for the new mean of a set of numbers with 40 added to it. To calculate the mean, we add all the numbers in the set together and then divide by the number of elements. The original set of numbers is {32, 16, 56, 40, 24, 45, 11}, and with the additional 40, this becomes {32, 16, 56, 40, 24, 45, 11, 40}. The sum of these numbers is 264 (which is the sum of the original set) + 40 = 304. There are now 8 numbers in the set, so we divide the total sum by 8 to get the mean.
So, the mean is 304 ÷ 8 = 38. None of the provided options (32.57, 33.71, 34.29, 35.14) match this result; therefore, there might be a mistake in the question or options presented, as the new mean of the set with the additional 40 is 38.