Question

predicting with experimental probability
a cereal manufacturer checks a set number of cereal boxes every day to better understand problems in the manufacturing process. the given table describes possible packaging problems and the frequency of each problem.
if the cereal manufacturer packages 10,000 boxes of cereal a day, about how many boxes would you expect to have too many raisins?
boxes

Explanation:

Step1: Calculate the experimental probability of too many raisins

The experimental probability \(P\) of an event is given by \(P=\frac{\text{Frequency of the event}}{\text{Total number of trials}}\).
For too many raisins, the frequency is \(20\) and the total number of trials (checked boxes) is \(1000\). So the experimental probability \(P=\frac{20}{1000}=0.02\)

Step2: Predict the number of boxes with too many raisins in \(10000\) - box production

If the probability of a box having too many raisins is \(P = 0.02\), and the number of boxes produced \(n=10000\).
We use the formula \(N = P\times n\). Substitute \(P = 0.02\) and \(n = 10000\) into the formula: \(N=0.02\times10000\)

Answer:

\(200\)