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
 (3 points) The number of hits on a certain
website follows a Poisson distribution with a mean rate of 4 per
minute.
 What is the probability that 5 messages are received in a given
minute? 0.1563
 What is the probability that 9 messages are received in 1.5
minutes? 0.0688
 What is the probability that fewer than 3 messages are received
in a period of 30 seconds?
0.6767
 (4 Points) A data center contains 1000
computer servers. Each server has probability 0.003 of failing on a
given day.
 What is the probability that exactly two servers fail?
0.224
 What is the probability that fewer than 998 servers function?
0.5768
 What is the mean number of servers that fail? How do you
interpret it? 3 per day
 What is the standard deviation of the number of servers that
fail? 1.732
 (4 points) Jim is a 60yearold 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 (116^{th}
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.
 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
 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
 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
 If Big Rock Insurance Company charges $5000 for the policy, how
much profit does the company expect to make? $2323.85
 (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
 at least 6 out of 10 business days. 0.837
 at most 3 of the 10 business days. 0.0547
 fewer than 7 out of 20 business days. 0.00647
 more than 16 out of 20 business days. 0.051
 What is the expected (mean) number of business days for which
the store would gross over $850 in a month (30 days)? 18 days