Video Transcript
A factory produces two types of
shirts: A and B. The table shows how many shirts of
each type were sold in five samples of 100 shirts from five different shopping
malls. If the factory sells 3,000 shirts,
how many of them do you expect to be of type A?
In order to answer this question,
we need to recall the formula for expected value. This is equal to the probability of
an event occurring multiplied by the number of trials or experiments. We will begin by calculating the
experimental probability of selecting a shirt of type A from the table. As there were five samples, one in
each shopping mall, of 100 shirts, we know that there were 500 shirts in total. Adding the values in the second row
of our table, we see that 227 of these shirts were of type A.
Whilst it is not required in this
question, it is worth noting that 273 of the shirts sold were of type B and that 227
plus 273 equals 500. Since probability is equal to the
number of successful outcomes over the total number of possible outcomes, where each
outcome is equally likely to be selected, we know that the probability that a shirt
from this sample was of type A is equal to 227 over 500. Since the factory sells 3,000
shirts, the expected value is equal to 227 over 500 multiplied by 3,000. Both 500 and 3,000 are divisible by
500. So our calculation simplifies to
227 multiplied by six, which is equal to 1,362.
We can conclude that from the
information in the sample that if the factory sold 3,000 shirts, we would expect
1,362 of them to be of type A.
