A national Italian restaurant has created a healthy option to one of its most popular dishes.
The original dish’s portion size has a mean $\mu$ of $1,500$ calories with a standard deviation of $50$ calories, and the healthy alternative’s portion size has a mean $\mu$ of $950$ calories with standard deviation of $25$ calories.
The resulting distribution of the calorie savings by choosing the healthy option over the original dish has a mean $\mu$ of $550$ calories saved and standard deviation $\sigma$ of $55.9$ calories. John and Mary go to the restaurant, and both order the healthy option.
What is the probability that their average calorie savings is equal to or greater than $600$ calories when John and Mary both opt for the healthier alternative?