Homework Assignment 3: (1) A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year, independent of any other employee. Determine the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance. (Ans 60) (2) Specifications for large batches of a certain item are that no batch shall contain more than 10% defectives. The inspection procedure is to draw 100 items out of the batch and reprocess the whole batch if there are 5 or more defectives in the sample. Find an upper bound for the probability that a bad batch is erroneously accepted. (Ans 0.024) (3) The number of accidents incurred by an insured driver in a given year has a Poisson distribution with parameter 2. If an accident occurs, the probability that the damage amount exceeds the deductible is
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