Final answer:
The mean, median, and mode are all the same in a normal distribution. The standard deviation is calculated using the sample standard deviation formula.
For a data set skewed right, the mean is greater than the median, which is greater than the mode.
Step-by-step explanation:
The question involves understanding the properties of a normal distribution and the calculation of measures like mean, median, mode, and standard deviation within the context of the given data set.
In a normal distribution, the mean, median, and mode are all equivalent and located at the peak of the curve. The standard deviation measures the spread of the data around the mean.
To compute the mean and standard deviation using the given dataset (10; 11; 15; 15; 17; 22), you would calculate the average of the numbers for the mean, and apply the sample formula for the standard deviation.
For instance, the mean of the given data set is 15. To find the standard deviation, you would use each data point's deviation from the mean, square it, sum these squared deviations, divide by the sample size minus one, and then take the square root.
If a data set is skewed right, the mode will be less than the median, which in turn will be less than the mean. If the distribution is skewed left, the mode will be greater than the median, which will be greater than the mean.
The number that is two standard deviations above the mean can be found by adding twice the standard deviation to the mean.
For example, if the mean is 15 and the standard deviation is 4.3, two standard deviations above the mean would be 15 + 2(4.3) = 23.6.