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Seven hundred tickets will be sold and these will be raffled during the fiesta of Brgy. Masiete. One of these tickets will win β±10,000 and the rest will win nothing. What will be the expected value and variance of your gain if you will buy one of the tickets?Β
An installation technician for a specialized communication system is dispatched to a
city only when three or more orders have been placed. Suppose orders follow a
Poisson distribution with a mean of 0.25 per week for a city of 100,000 and suppose
your city contains a population of 800,000.
a) What is the probability that a technician is required after a one-week period?
b) If you are the first one in the city to place an order, what is the probability that you
have to wait more than two weeks from the time you place your order until a
technician is dispatched?
A local drugstore owner knows that, on average, 100 people enter his store each hour.
a) Find the probability that in a given 3-minute period nobody enters the store.
b) Find the probability that in a given 3-minute period more than 5 people enter the
store.
The number of telephone calls that arrive at a phone exchange is often modeled as a
Poisson random variable. Assume that on the average there are 10 calls per hour.
a) What is the probability that there are exactly 5 calls in one hour?
b) What is the probability that there are there are exactly 15 calls in two hours?
c) What is the probability that there are exactly 5 calls in 30 minutes?
Suppose that the number of customers that enter a bank in an hour is a Poisson
random variable, and suppose that π(π = 0) = 0.05. Determine the mean and
standard deviation of π.
Service calls come to a maintenance center according to a Poisson process, and on
average, 2.7 calls are received per minute. Find the probability that
a) no more than 4 call in any minute;
b) fewer than 2 calls come in any minute;
c) more than 10 calls come in a 5-minute period.
Potholes on a highway can be a serious problem, and are in constant need of repair.
With a particular type of terrain and make of concrete, past experience suggests that
there are, on the average, 2 potholes per mile after a certain amount of usage. It is
assumed that the Poisson process applies to the random variable βnumber of
potholes.β
a) What is the probability that no more than one pothole will appear in a section of
1 mile?
b) What is the probability that no more than 4 potholes will occur in a given section
of 5 miles?
The number of failures of a testing instrument from contamination particles on the
product is a Poisson random variable with a mean of 0.02 failure per hour.
a) What is the probability that the instrument does not fail in an 8-hour shift?
b) What is the probability of at least one failure in a 24-hour shift?
For a certain type of copper wire, it is known that, on the average, 1.5 flaws occur per
millimeter. Assuming that the number of flaws is a Poisson random variable, what is
the mean number of flaws in a portion of length 5 millimeters? What is the
probability, in 4 significant figures, that no flaws occur in a certain portion of wire of
length 5 millimeters?
The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean π = 7. Compute the probability that more than 10 customers will arrive in a 2-hour period.
