Question

at a large factory, the boxes of cereal are marked 32 oz. the actual amount in boxes varies slightly per box. the process that dispenses cereal into the boxes has a roughly normal distribution with a mean of 32.4 ounces and standard deviation of 0.4 ounces. what percentage of the boxes contain more than 33.18 ounces?
which is the correct graph for the above percentage?
% (give your answer to 2 decimal places. be careful, the answer is in percent form)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 33.18\), \(\mu=32.4\), and \(\sigma = 0.4\).

$$z=\frac{33.18 - 32.4}{0.4}=\frac{0.78}{0.4}=1.95$$

Step2: Find the probability using the standard normal table

We want to find \(P(X>33.18)\), which is equivalent to \(P(Z > 1.95)\) since \(z=\frac{X-\mu}{\sigma}\).
Using the property \(P(Z>z)=1 - P(Z\leq z)\), and from the standard normal table \(P(Z\leq1.95)=0.9744\)

$$P(Z > 1.95)=1 - 0.9744 = 0.0256$$

Step3: Convert the probability to a percentage

To convert the probability to a percentage, we multiply by 100.

$$0.0256\times100 = 2.56\%$$

Answer:

\(2.56\%\)