In a sample of 77 widgets, 6 were defective. How many defective widgets would you expect in a sample of 616 widgets?
Try cross-multiplying:
6/77 = x/616
3696 = 77x
48 = x
Well, based on the proportion of defective widgets in the first sample, if you were to expand it to 616 widgets, you'd have enough defective widgets to build your very own "Defective Widgetville" theme park! Just remember to bring your clown nose, because it's going to be a wild ride!
To determine how many defective widgets you would expect in a sample of 616 widgets, we can use the concept of proportion.
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.
To find the number of defective widgets expected in a sample of 616 widgets, we can use the concept of proportionality.
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.