To determine how many boxes would be expected to have too many raisins, given that 10,000 cereal boxes are packaged each day, follow these steps:
1. Identify the frequency of each problem from the table:
- Frequency of box printing error: 5
- Frequency of underweight box: 10
- Frequency of boxes with too many raisins: 20
- Frequency of boxes with no problems: 965
- Total frequency: 1000
2. Calculate the percentage of boxes with too many raisins:
Percentage of boxes with too many raisins = [tex]\(\frac{\text{Frequency of boxes with too many raisins}}{\text{Total frequency}}\)[/tex] [tex]\(\times\)[/tex] 100.
So,
[tex]\[
\text{Percentage of boxes with too many raisins} = \frac{20}{1000} \times 100 = 2\%
\][/tex]
3. Determine the total number of boxes packaged each day:
The manufacturer packages 10,000 boxes of cereal each day.
4. Calculate the expected number of boxes with too many raisins:
Expected number of boxes with too many raisins = [tex]\(\text{Percentage of boxes with too many raisins}\)[/tex] [tex]\(\times\)[/tex] [tex]\(\text{Total boxes packaged each day}\)[/tex] [tex]\(\div\)[/tex] 100.
So,
[tex]\[
\text{Expected number of boxes with too many raisins} = \frac{2 \times 10000}{100} = 200
\][/tex]
Therefore, you would expect about 200 boxes to have too many raisins out of the 10,000 boxes packaged each day.
