Final answer:
In a symmetrical distribution, the mean, median, and mode are all equal. The correct answer is a. The mean is 51 Correct.
Step-by-step explanation:
The relationship among the mean, median, and mode in a symmetrical distribution (such as a normal distribution) is that they are all equal. In other words, the mean, median, and mode will have the same value.
So, in the case of the given normal distribution, since the mean is 51, the median and mode will also be 51.
When working with a normal distribution, the mean, median, and mode are all located at the same point on the graph. This point is the center of the symmetrical bell curve. Assuming the mean is given as 51, we can say that both the median and mode are also 51 in a perfect normal distribution.
To calculate the mean of the provided data set (10; 11; 15; 15; 17; 22), you sum all the numbers and divide by the number of values. The mean is 15.
Calculating the standard deviation involves finding the square root of the average of the squared deviations from the mean, which, using the sample formula, gives us a standard deviation of 4.3. If we want to find a value that is two standard deviations above this mean, we would calculate 15 + 2 * 4.3, which equals 23.6.