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.
