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 $1{,}500\text{ calories}$ with a standard deviation of $50\text{ calories}$, and the healthy alternative’s portion size has a mean $\mu$ of $950\text{ calories}$ with standard deviation of $25\text{ calories}$.

The resulting distribution of the calorie savings by choosing the healthy option over the original dish has a mean $\mu$ of $550\text{ calories}$ saved and standard deviation $\sigma$ of $55.9\text{ calories}$. 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 $600\text{ calories}$ when John and Mary both opt for the healthier alternative?