# MATHEMATICS

 1)      An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of 3.3 emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution.

 (a) What is the probability Linda Lahey, company president, received exactly 4 emails between 4 P.M. and 5 P.M. yesterday? (Round your answer to 4 decimal places.)

 Probability [removed]

 (b) What is the probability she received 7 or more emails during the same period? (Round your answer to 4 decimal places.)

 Probability [removed]

 (c) What is the probability she received one or less emails during the period? (Round your answer to 4 decimal places.)

 Probability [removed]

 2)      Recent crime reports indicate that 4.0 motor vehicle thefts occur each minute in the United States. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution.

 (a) Calculate the probability exactly four thefts occur in a minute.(Round your answer to 3 decimal places.)

 Probability [removed]

 (b) What is the probability there are no thefts in a minute? (Round your answer to 3 decimal places.)

 Probability [removed]

 (c) What is the probability there is one or less theft in a minute? (Round your answer to 3 decimal places.)

 Probability [removed]

 3)      New Process Inc. a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than 6 unfilled orders on hand at the end of 95 percent of the working days. Frequent checks of the unfilled orders at the end of the day reveal that the distribution of the unfilled orders follows a Poisson distribution with a mean of 3.1 orders.

 (a) Has New Process Inc. lived up to its internal goal? (Round your answer to 5 decimal places.)

 P(X< 6 | μ = 3.1) [removed]

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