A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution, with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight?
A)31.60 oz
B)31.85 oz
C)34.15 oz
D)34.40 oz

Question

Quizplus · Accepted Answer

To find the weight that is considered overweight (top 5%), we look for the z-score corresponding to the top 5% in a standard normal distribution. The z-score for the top 5% is approximately 1.645. Using the z-score formula $z = \frac{X - \mu}{\sigma}$, where $X$ is the value we're looking for, $\mu = 33$ oz is the mean, and $\sigma = 0.7$ oz is the standard deviation, we can solve for $X$: $1.645 = \frac{X - 33}{0.7}$. Solving for $X$ gives $X = 1.645 \times 0.7 + 33 \approx 34.15$ oz.

A Company Produces Packets of Soap Powder Labeled "Giant Size