Question

The meat department at a local supermarket specifically prepares its "1-pound" packages of ground beef so that there will be a variety of weights, some slightly more and some slightly less than 1 pound. Suppose that the weights of these "1-pound" packages are normally distributed with a standard deviation of 0.15 pound. What is the probability that a randomly selected package of ground beef will weigh less than 0.80 pound?

Answer 1

Let X be the weight of package, $X\sim N\left( 1,0.15^2 \right)$

Then

$P\left( X\leqslant 0.8 \right) =P\left( \frac{X-1}{0.15}\leqslant \frac{0.8-1}{0.15} \right) =P\left( Z\leqslant -1.33333 \right) =\\=\varPhi \left( -1.33333 \right) =0.0912$