Question Video: Using Experimental Probability to Determine the Expected Number of Outcomes of an Event Mathematics • 7th Grade

A factory produces 8,000 shirts each day. At the end of a day, 1,600 shirts were inspected and 50 were found to be defective. What is the expected number of defective shirts produced that day?

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Video Transcript

A factory produces 8,000 shirts each day. At the end of a day, 1,600 shirts were inspected and 50 were found to be defective. What is the expected number of defective shirts produced that day?

In order to answer this question, we need to recall the expected value formula. This states that the expected value is equal to the probability of an event occurring multiplied by the number of trials or experiments. In this question, this will be equal to the probability that a shirt is defective multiplied by the number of shirts produced.

We begin by calculating the experimental probability that a shirt was defective. Recalling that probability is the number of successful outcomes over the total number of outcomes, where each outcome is equally likely to be selected, we have the probability that a shirt is defective is 50 over 1,600, since 50 shirts out of the sample of 1,600 were defective. The factory produces 8,000 shirts per day. So we need to multiply 50 over 1,600 by 8,000. 1,600 and 8,000 are both divisible by 1,600. So our calculation simplifies to 50 multiplied by five, which is equal to 250.

We can therefore conclude that we would expect the number of defective shirts produced by the factory that day to be 250.

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