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Question:

A toy manufacturer makes 15,000 toys a year. The company randomly selects 300 of the toys to sample for inspection. The company discovers that there are 5 faulty toys in the sample. Based on the sample, how many of the 15,000 total toys are likely to be faulty?

A 250
explanation

The sample indicates that 5 out of every 300 randomly selected toys will be faulty. Consequently, a proportion can be set up that relates the unknown number of faulty toys in the total number of toys to the ratio of faulty toys to the sample: \( \frac{\mathrm{5} }{\mathrm{300}} = \frac{\mathrm{T} }{\mathrm{15000}} \)
T is the unknown number of faulty toys in the total. Multiply both sides by 15,000 and then divide the left side by 300 to solve for T: \(\frac{\mathrm{15000 \times 5} }{\mathrm{300}} = T\)
\(\frac{\mathrm{50 \times 5} }{\mathrm{1}} = T = 250\)