Answers to the questions must be in clear and understandable English. Any R code and output that you add must be clearly identifiable as R code or output,

1 Red versus blue
A candy factory in Hoboken performs tests to determine whether their candy packets are evenly
distributed between red and blue candies. For each batch of 100,000 packets, 100 packets are
opened to determine whether there are red candies or blue candies in the packet. If fewer than 45
or more than 55 packets have red candies, the batch is considered to be unevenly distributed.
(a) 4 Suppose that in a particular batch of packets, 40% of these packets contain red candies.
What is the probability that this batch passes the quality test?
(b) 4 Suppose that for a particular test, 52 patches have red candies. Give a 99% confidence
interval for the percentage packets with red candies in the batch.
The factory feels that its quality assurance process is needlessly destructive and is looking for ways
to reduce the number of packets that are sent to be tested. To meet equality standards, however,
any batch with fewer than one third of the packets containing red (or blue) candies should be
rejected by the quality assurance process with a probability of 99%.
(c) 2 How many packets should be tested to give a 100% guarantee that a batch has at least
one third red candy packets and at least one tird blue candy packets? Explain your answer
(d) 5 A manager suggests to test 20 packets per batch, and rejecting the batch if the number
of packets with red candies is anything other than 10. Would this procedure meets equality
standards? Explain your answer
(e) 10 What is the minimum number of packets that have to be tested in order to meet the
factory’s equality standards?
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