Answer to Question #302143 in Statistics and Probability for viky

Question

The Surf-excel company uses a machine to fill boxes with soap powder. Assume that the net weight of the boxes of soap is normally distributed with mean 15 ounces and standard deviation 0.8 ounces. 25% of the boxes will be heavier than a certain net weight w and 75% of the boxes will be lighter than this net weight. Find w

Answer 1

Let $W=$ the net weight of the box: $W\sim N(\mu, \sigma).$

Given $\mu=15\ ounces, \sigma=0.8\ ounces.$

$$P(W<w)=P(Z<\dfrac{w-15}{0.8})=0.75$$

$$\dfrac{w-15}{0.8}\approx0.67449$$

$$w=15.54\ ounces$$