Final answer:
The minimum value for the upper quartile for the sum of a sample can be calculated using the formula Q3 = nQ - IQR, where Q is the median, n is the sample size, and IQR is the interquartile range.
Step-by-step explanation:
The random variable σx represents the sum of a sample, which is the sum of the individual values in the sample. In this case, the sample is formed by randomly selecting 25 values from a distribution with a mean of 70 and a standard deviation of 13. To find the minimum value for the upper quartile for σx, we need to calculate the upper quartile for the sum of 25 values from this distribution.
The formula to calculate the upper quartile for the sum of a sample is Q3 = nQ − IQR, where Q is the median, n is the sample size, and IQR is the interquartile range. In this case, Q is the median of the distribution, which is 70, n is 25, and IQR can be calculated as 1.5 times the standard deviation, which is 1.5 * 13 = 19.5. Therefore, the upper quartile for σx is Q3 = 25(70) − 19.5 = 1750 − 19.5 = 1730.5 (rounded to two decimal places).