Question

The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 130 gallons and standard deviation 12 gallons. On a randomly selected day, the probability that the store sells more than 154 gallons is

Answer 1

$\mathbb P(X>154)=\mathbb P\left(\dfrac{X-130}{12}>\dfrac{154-130}{12}\right)=\mathbb P(Z>2)$

Since approximately 95% of any normal distribution falls within two standard deviations of the mean, it follows that 5% falls outside that range, with 2.5% to either side. So $\mathbb P(Z>2)\approx0.025$.

The actual value is a bit closer to 0.0228, but that's not very far off.