Answer to Question #267308 in Statistics and Probability for John

Question

A company that manufactures and bottles apple juice uses a machine that automatically fills 16-ounce bottles. There is some variation, however, in the amounts of liquid dispensed into the bottles that are filled. The amount dispensed has been observed to be approximately normally distributed with mean 16 ounces and standard deviation 1 ounce.

(a) Determine the proportion of bottles that will have more than 17 ounces dispensed into them.

Answer 1

(a) Let $X=$the amount of liquid dispensed into the bottle: $X\sim N(\mu, \sigma^2).$

Given $\mu=16, \sigma=1$

$$P(X>17)=1-P(X\leq 17)$$

$$=1-P(Z\leq \dfrac{17-16}{1})=1-P(Z\leq1)$$

$$\approx0.158655$$