Final answer:
Without the specific data on mortgage amounts, the standard deviation cannot be calculated. However, the probability of average values and the relationship between correlation and coefficient of determination can be discussed based on statistical principles like the Central Limit Theorem and properties of the normal distribution.
Step-by-step explanation:
To calculate the standard deviation of the average outstanding mortgage amounts for all 50 states, one would need individual state data, which is not provided. Therefore, without the raw data, the standard deviation cannot be directly calculated. However, to address some of the concepts mentioned, it is indeed possible for the standard deviation to be greater than the average if there is a wide spread or variability in the data. When discussing the sample mean, the distribution of the sample mean will approach a normal distribution as the sample size gets larger due to the Central Limit Theorem, assuming the data is independent and identically distributed.
For instance, if the average salary is considered, it is more likely to find the average salary of 1,000 residents to be within a range closer to the mean ($2,000 to $2,100) than further from it ($2,100 to $2,200), because salaries would tend to cluster around the mean according to the characteristics of a normal distribution.
In the scenario of a correlation necessary to have a coefficient of determination of at least 0.50, the required correlation would be at least 0.71 or -0.71, since the coefficient of determination is the square of the correlation coefficient (0.712 ≈ 0.50).