Try cross-multiplying:
6/77 = x/616
3696 = 77x
48 = x
6/77 = x/616
3696 = 77x
48 = x
Let's first find the proportion of defective widgets in the initial sample of 77 widgets:
Proportion of defective widgets = (Number of defective widgets / Total number of widgets)
In the initial sample of 77 widgets, there were 6 defective widgets:
Proportion of defective widgets = (6 / 77) = 0.0779
Now, to find the expected number of defective widgets in a sample of 616 widgets, we can multiply the proportion by the total number of widgets in the new sample:
Expected number of defective widgets = Proportion of defective widgets * Total number of widgets
Expected number of defective widgets = 0.0779 * 616
Expected number of defective widgets = 47.9764
Therefore, you would expect approximately 48 defective widgets in a sample of 616 widgets.
First, we need to calculate the proportion of defective widgets in the initial sample of 77 widgets. This can be calculated by dividing the number of defective widgets by the total number of widgets in the sample:
Proportion of defective widgets = Number of defective widgets / Total number of widgets
Proportion of defective widgets = 6 / 77
Next, we can use this proportion to estimate the expected number of defective widgets in a sample of 616 widgets. To do this, we multiply the proportion by the total number of widgets in the new sample:
Expected number of defective widgets = Proportion of defective widgets × Total number of widgets
Expected number of defective widgets = (6 / 77) × 616
Now, we can calculate the expected number of defective widgets:
Expected number of defective widgets = (6 / 77) × 616
Expected number of defective widgets ≈ 47.83
Therefore, you would expect approximately 47.83 defective widgets in a sample of 616 widgets. However, since we cannot have a fraction of a widget, we round this to the nearest whole number. Hence, the final answer would be approximately 48 defective widgets.