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can you please work on this assignment because I am having some issues with it. I...

can you please work on this assignment because I am having some issues with it. I have it completed I would just like to know if everything is correct.  

DISCRETE PROBABILITY DISTRIBUTIONS

  1. (3 points) The number of hits on a certain website follows a Poisson distribution with a mean rate of 4 per minute.
  1. What is the probability that 5 messages are received in a given minute? 0.1563
  2. What is the probability that 9 messages are received in 1.5 minutes? 0.0688
  3. What is the probability that fewer than 3 messages are received in a period of 30 seconds?

0.6767

  1. (4 Points) A data center contains 1000 computer servers. Each server has probability 0.003 of failing on a given day.

  1. What is the probability that exactly two servers fail? 0.224

  1. What is the probability that fewer than 998 servers function? 0.5768

  1. What is the mean number of servers that fail? How do you interpret it? 3 per day

  1. What is the standard deviation of the number of servers that fail? 1.732

  1. (4 points) Jim is a 60-year-old male in reasonably good health. He wants to take out a $50,000 term (that is, straight death benefit) life insurance policy until he is 65. The policy will expire on his 65th birthday. The probability of death in a given year is provided by the Vital Statistics Section of the Statistical Abstract of the United States (116th edition)

X=age

60

61

62

63

64

P(death at this age)

0.01191

0.01292

0.01396

0.01503

0.011613

Jim is applying to Big Rock Insurance Company for his term insurance policy.

  1. What is the probability that Jim will die in his 60th year? Using this probability and the $50,000 death benefit, what is the expected cost to Big Rock Insurance? 0.01191 $595.50

  1. Repeat part (a) for years 61, 62, 63, and 64. What would be the total expected cost to Big Rock Insurance over the years 60 through 64? 61: $646.00 62: $698.00 63: $751.50 64: $806.50

  1. If Big Rock Insurance wants to make a profit of $700 above the expected total cost paid out for Jim’s death, how much should it charge for the policy? $4197.50

  1. If Big Rock Insurance Company charges $5000 for the policy, how much profit does the company expect to make? $2323.85

  1. (5 points) Trevor is interested in purchasing the local hardware/electronic goods store in a small town in South Ohio. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 60% of the business days it is open.

Estimate the probability that the store will gross over $850

  1. at least 6 out of 10 business days.   0.837

  1. at most 3 of the 10 business days. 0.0547

  1. fewer than 7 out of 20 business days. 0.00647

  1. more than 16 out of 20 business days. 0.051

  1. What is the expected (mean) number of business days for which the store would gross over $850 in a month (30 days)? 18 days

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