Question

Give me some sugar! Machines that fill bags with powdered sugar are supposed to

dispense $32$ounces of powdered sugar into each bag. Let $x=$the weight (in ounces) of the

powdered sugar dispensed into a randomly selected bag. Suppose that $x$can be modeled

by a Normal distribution with mean $32$ounces and standard deviation $0.6$ounce. Find $P(x\le 31)$. Interpret this value.

Short answer

About$4.75\%$of all bags contain less than$31$ounces.

Step-by-step solution

Step 1. Given information. 

We have given values of mean$\mu =32$, standard deviation$\sigma =0.6$and$x=9$.

Step 2. To find the probability. 

The z- score is the value decreased by the mean, divided by the standard deviation

$$\begin{gathered} z=\frac{x-\mu }{\sigma } \\ =\frac{31-32}{0.6} \\ \approx -1.67 \end{gathered}$$

Now,

$$\begin{gathered} P(x\le 31)=P(Z<-1.67) \\ =0.0475 \\ =4.75\% \end{gathered}$$