A 2-column table with 5 rows. Column 1 is labeled Packaging Problems with entries box printing error, underweight box, too many raisins, no problems, total. Column 2 is labeled Frequency with entries 5, 10, 20, 965, 1,000.

Question

A cereal manufacturer checks a set number of cereal boxes every day to better understand problems in the manufacturing process. The table at right 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

Answer 1

To find out how many boxes would be expected to have "too many raisins," we first need to determine the proportion of packaging problems represented by "too many raisins" from the provided data in the table.

From the table:

• The frequency of "too many raisins" is 20.
• The total frequency of all problems is 1,000.

The proportion of boxes with too many raisins can be calculated as follows:

\[ \text{Proportion of too many raisins} = \frac{\text{Frequency of too many raisins}}{\text{Total frequency}} = \frac{20}{1000} = 0.02 \]

Next, we multiply this proportion by the total number of boxes packaged each day (10,000):

\[ \text{Expected boxes with too many raisins} = \text{Proportion of too many raisins} \times \text{Total boxes} = 0.02 \times 10000 = 200 \]

Thus, you would expect about 200 boxes to have too many raisins.