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Historical data suggests that a scientific journal accepts 10% of the manuscripts it receives, rejects 50% of the manuscripts it receives, and requests "revise and resubmit" for the remaining manuscripts. In a given month, the journal receives 75 manuscripts.
(a) What is the probability that 5 are accepted and 40 are rejected?
(b) What is the probability that 5 are accepted?
(c) What is the expected value of the accepted manuscripts?
(d) What is the standard deviation of the rejected manuscripts?
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