Final answer:
Interval estimation procedures generate intervals that can contain the population mean, median, mode, and other parameters, depending on the chosen confidence level. For a symmetrical distribution, mean, median, and mode are equal. To calculate the mean and standard deviation for a data set, one uses the sum of the values divided by their count and a formula incorporating deviations from the mean, respectively.
Step-by-step explanation:
The probability that the interval estimation procedure will generate an interval that contains the true population parameter depends on the confidence level selected. For example, if a 90% confidence interval is constructed, it implies that if we took repeated samples and from each calculated a confidence interval, approximately 90 percent of these intervals would contain the population mean (or other parameter of interest). This interval has a general form, represented as (lower bound, upper bound) = (point estimate - EBM, point estimate + EBM), where 'EBM' stands for Error Bound for the Mean, and the point estimate is commonly the sample mean.
When considering a symmetrical distribution, the mean, median, and mode all coincide at the same point. In exercise 52, calculating the mean and standard deviation involves adding all the values and dividing by the total number of values for the mean, and for the standard deviation, using the sample formula. For the given data set (10, 11, 15, 15, 17, 22), the mean would be calculated as the sum of all numbers divided by 6. Based on that mean and the calculated standard deviation, the number two standard deviations above the mean is found by adding twice the standard deviation to the mean.