Question

A manufacturer inspects 1000 bicycles at random. He finds that 98 of them have no defects. There are 2400 bicycles in the warehouse. Predict how many bicycles are likely to not have a defect.

Answer 1

We calculated the proportion of non-defective bicycles from the sample and applied that proportion to the entire warehouse inventory, predicting that approximately 2165 bicycles out of the 2400 in the warehouse are likely to have no defect.

Step-by-step explanation:

The question asks us to predict how many bicycles out of the 2400 in the warehouse are likely to have no defect, based on a sample of 1000 bicycles where 98 were found to have no defects. We can assume that the sample is representative of the population in the warehouse. Therefore, we calculate the proportion of bicycles without defects in the sample and apply that proportion to the entire warehouse inventory.

To calculate the proportion of non-defective bicycles in the sample:

• Number of non-defective bicycles in sample = 1000 - 98 = 902
• Proportion of non-defective bicycles = 902 / 1000 = 0.902

To predict the number of non-defective bicycles in the warehouse:

• Total number of bicycles in warehouse = 2400
• Proportion of non-defective bicycles × Total number of bicycles = 0.902 × 2400
• Number of non-defective bicycles expected in warehouse = 2164.8

Therefore, we can predict that approximately 2165 bicycles in the warehouse are likely to have no defect.