Question

Suppose that x is normally distributed with mean 110 and standard deviation 30.

Answer 1

Standard the random variable $X$ using the transformation

$Z=\dfrac{X-\mu}\sigma$

where $\mu$ and $\sigma$ are the mean and standard deviation of $X$, respectively.

$\mathbb P(X\ge170)=\mathbb P\left(\dfrac{X-110}{30}\ge\dfrac{170-110}{30}\right)=\mathbb P(Z\ge2)$

Now, you can recall that for any normal distribution, approximately 95% of its data falls within 2 standard deviations of the mean, so to either side, there is approximately 2.5% of data that falls below 2 standard deviations from the mean, and 2.5% that falls $2\sigma$ above $\mu$. In other words, $\mathbb P(Z\ge2)\approx0.025$.