Step 1 :The mathematical statement $X \sim N(70,100)$ means that X follows a normal distribution with a mean of 70 and a variance of 100.
Step 2 :The standard deviation is the square root of the variance, so the standard deviation is 10.
Step 3 :To find $P(X>50)$, we need to calculate the cumulative distribution function (CDF) at 50 and subtract it from 1. This is because the CDF at a point x gives the probability that X is less than or equal to x. So, $1 - CDF(50)$ gives the probability that X is greater than 50.
Step 4 :Using the mean of 70 and standard deviation of 10, we find that $P(X>50) \approx 0.977$.
Step 5 :Final Answer: $P(X>50) \approx \boxed{0.977}$