Question

The number of accidents in a certain city is modeled by a Poisson random variable with average rate of 10 accidents per day. Suppose that the number of accidents in different days are independent. Use the central limit theorem to find the probability that there will be more than 3800 accidents in a certain year. Assume that there are 365 days in a year

Answer #1

Question 5. Suppose that the number of accidents in a city on a
rainy day is a Poisson random variable with mean 8, on a cloudy day
is a Poisson random variable with mean 5 and on a sunny day is a
Poisson random variable with mean 2. If the probability that it
will be rainy tomorrow is 0.4, the probability that it will be
cloudy tomorrow is 0.3 and the probability that it will be sunny
tomorrow is 0.3;...

The number of traffic accidents at a certain intersection is
thought to be well modeled by a Poisson process with a mean of 3.5
accidents per year
If no accidents have occurred within the last six months, what
is the probability that an accident will occur within the next
year?

There are an average of 7 automobile accidents involving serious
personal injuries in the City of Austin every day. The number of
daily automobile accidents involving serious personal injuries in
the City of Austin, X, is
distributed as a Poisson random variable.
a) What is the probability that there will be at least 15
automobile accidents involving serious personal injuries in the
City of Austin tomorrow? ______
b) What is the probability that there will be at least 10 but...

The number of errors in each of 300 files has a Poisson
distribution with 1.4 errors per file on average. Assume the errors
in different files are independent. Use the Central Limit Theorem
to approximate the probability that the total number of errors
exceeds 400.

8. The city of Fastville has been experiencing a mean of 73 car
accidents per year.
1) Find the probability that on a given day the number of car
accidents in Fastville is 2. (Assume 365 days in a year.) Round
your answer to four decimal places.
2) Find the probability that on a given day the number of car
accidents in Fastville is more than one. Round your answer to four
decimal places.
3) Find the minimum and the...

The number of traffic accidents in a certain area follows a
Poisson process with a rate of 1.5 per hour between 8:00 A.M. and
5:00 P.M. during the normal working hours in a working day. Compute
the following probabilities.
There will be no traffic accident between 11:30 AM to 12:00
PM.
There will be more than 3 traffic accidents after 3:45
P.M.
There will be in between 15 and 18 traffic accident during the
normal working hours in a working...

the number of accidents on a particular highway average 4.4 per
year. assume that the number of accidents follows a Poisson
distribution. what is the probability that there are exactly four
accidents next year? what is the probability that there are more
than three accidents next year?

Number of visits to an emergency center is modeled as a Poisson
process with average number of arrivals being 6 per hour. What is
the probability that it will take more than 15 minutes for the next
two arrivals?

1. Given a poisson random variable, X = # of events that occur,
where the average number of events in the sample unit (μ) is given
on the right, determine the smallest critical value (critical value
= c) for the random variable such that you have at least a 99%
probability of finding c or fewer events.
μ = 4
2. Given a binomial random variable X where X = #
of operations in a local hospital that...

Note: Use statistical tables when it is possible The number of
accidents at an intersection follows Poisson distribution with an
average of three accidents per day. Find (Round to THREE decimal
places) 1. The probability of an accident-free day. 2. The
probability that there is at most 14 accidents in five days. 3. The
accepted number of accident-free days in January 4. The probability
that there are four accident-free days in January Calculate \mu and
\sigma 2 ? 5. Suppose...

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