A random sample of 50 was taken from a shipment of 12,500 light bulbs. There were 2 broken bulbs in the sample. How many broken bulbs would you expect in the entire shipment?
2/50 = x/12500
Solve for x.
To estimate the number of broken bulbs in the entire shipment, we can use the concept of proportion.
First, we calculate the proportion of broken bulbs in the sample. In this case, we have a sample size of 50 light bulbs and 2 of them are broken. Therefore, the proportion of broken bulbs in the sample is 2/50, which simplifies to 0.04 or 4%.
Next, we can use this proportion to estimate the number of broken bulbs in the entire shipment. Since the proportion of broken bulbs in the sample is 4%, we can assume that the same proportion holds true for the entire shipment.
To find the number of broken bulbs in the entire shipment, we multiply the proportion of broken bulbs (0.04) by the total number of light bulbs in the shipment (12,500):
0.04 * 12,500 = 500 broken bulbs
Therefore, we would expect around 500 broken bulbs in the entire shipment.