A farmer is using a random sample to predict the number of broken eggs in a shipment of 3,000 eggs. Using a calculator, the farmer generates the following random numbers. The numbers 1-250 represent broken eggs.
477, 2116, 1044, 81, 619, 755, 2704, 900, 238, 1672, 187, 1509.
Based on this sample, how many broken eggs might the farmer expect?
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To determine how many broken eggs the farmer might expect based on the sample, we need to count the number of random numbers within the range that represents broken eggs (1-250) in the given list.
Let's go through the list of random numbers and count how many fall within the range of broken eggs (1-250):
477 - Does not fall within the range.
2116 - Does not fall within the range.
1044 - Does not fall within the range.
81 - Falls within the range.
619 - Does not fall within the range.
755 - Does not fall within the range.
2704 - Does not fall within the range.
900 - Does not fall within the range.
238 - Falls within the range.
1672 - Does not fall within the range.
187 - Falls within the range.
1509 - Does not fall within the range.
Out of the 12 randomly generated numbers, 3 fall within the range of broken eggs (1-250).
To determine the estimated number of broken eggs in the shipment, we can use the ratio of broken eggs in the sample to the total sample size. The ratio is 3/12 (3 broken eggs out of 12 random numbers).
To calculate the expected number of broken eggs:
Expected number = (Ratio of broken eggs) * (Total number of eggs in the shipment)
In this case, the total number of eggs in the shipment is 3,000. Using the ratio, we can calculate the expected number of broken eggs:
Expected number of broken eggs = (3/12) * 3000 = 750
Based on this sample of random numbers, the farmer might expect around 750 broken eggs in the shipment of 3,000 eggs.
From these numbers it seems that 3/12 would be broken so that is 1/4 or 25%.
Multiply 3000 times .25 to find out how many might be broken.