Question

A quality control

inspector noticed that 3 out of
the last 15 toasters he checked
had defects. Considering this
data, how many of the next 20
toasters he checked should he
expect to have defects.

Answer 1

Explanation:

To determine how many of the next 20 toasters the quality control inspector should expect to have defects based on the observed defect rate, you can use the proportion of defective toasters found in the sample.

The observed defect rate is 3 out of 15 toasters checked, which can be written as:

\[ \text{Defect rate} = \frac{\text{Number of Defective Toasters}}{\text{Total Number of Toasters Checked}} = \frac{3}{15} \]

Now, you can use this defect rate to estimate the number of defective toasters in the next 20 toasters:

\[ \text{Expected Defective Toasters} = \text{Defect rate} \times \text{Total Number of Toasters to be Checked} \]

Substitute the values:

\[ \text{Expected Defective Toasters} = \left(\frac{3}{15}\right) \times 20 \]

Now, calculate:

\[ \text{Expected Defective Toasters} = \frac{3}{15} \times 20 = \frac{1}{5} \times 20 = 4 \]

So, based on the observed defect rate, the quality control inspector should expect 4 out of the next 20 toasters to have defects.