Since \(700=500+2\times100=\mu+2\sigma\) is 2 standard deviations above the mean, you're looking for the probability that
\(\mathbb P(0
The empirical rule says that approximately 95% of a normal distribution lies within 2 standard deviations of the mean, or \(\mathbb P(|Z|<2)\approx0.98\).
Since the normal distribution is symmetric, you have
\(\mathbb P(|Z|<2)=2\mathbb P(0
