A soap factory randomly inspects 100 bars of soap to better identify problems that occur during the manufacturing process. The table below displays the possible problems and frequency for each.

Question

Soap Problems
Frequency
Underweight
4
Impurities
2
Broken bar
3
None
91
Total
100

If the soap factory makes 5,000 bars of soap per day, how many of those bars would they expect to be broken?
They would expect 100 bars to be broken.
They would expect 150 bars to be broken.
They would expect 300 bars to be broken.
They would expect 450 bars to be broken

Answer 1

To find out how many broken bars of soap the factory would expect to produce in a day, we first need to determine the proportion of broken bars from the inspected sample.

From the provided data, we see that there were 3 broken bars out of 100 inspected bars.

To find the probability of a bar being broken, we calculate:

\[ \text{Probability of broken bar} = \frac{\text{Number of broken bars}}{\text{Total bars inspected}} = \frac{3}{100} = 0.03 \]

Now, to find the expected number of broken bars in a day when the factory produces 5,000 bars, we apply this probability:

\[ \text{Expected number of broken bars} = \text{Total bars produced} \times \text{Probability of broken bar} \] \[ \text{Expected number of broken bars} = 5000 \times 0.03 = 150 \]

Therefore, the factory would expect 150 bars to be broken.