Question

**Q2)** Consider a Poisson probability
distribution with λ=4.9. Determine the following probabilities.

a) exactly 5 occurrences

b) more than 6 occurrences

c) 3 or fewer occurrences

**Q3)** Consider a Poisson probability
distribution. Determine the probability of exactly six occurrences
for the following conditions.

a) λ=2.0

b) λ=3.0

c) λ=4.0

d) What conclusions can be made about how these probabilities change with λ?

**Q4)** A particular intersection in a small town
is equipped with a surveillance camera. The number of traffic
tickets issued to drivers passing through the intersection follows
the Poisson distribution and averages 5.3 per month.

a. What is the probability that 5 traffic tickets will be issued at the intersection next month?

b. What is the probability that 3 or fewer traffic tickets will be issued at the intersection next month?

c. What is the probability that more than 6 traffic tickets will be issued at the intersection next month?

**Q5)** A customer support center for a computer
manufacturer receives an average of 2.6 phone calls every five
minutes. Assume the number of calls received follows the Poisson
distribution.

a. What is the probability that no calls will arrive during the next five minutes?

b. What is the probability that 3 or more calls will arrive during the next five minutes?

c. What is the probability that 3 calls will arrive during the next ten minutes?

d. What is the probability that no more than 2 calls will arrive during the next ten minutes?

**Q6)** Production records indicate that 3.3% of
the light bulbs produced in a facility are defective. A random
sample of 35 light bulbs was selected.

a. Use the binomial distribution to determine the probability that fewer than three defective bulbs are found.

b. Use the Poisson approximation to the binomial distribution to determine the probability that fewer than three defective bulbs are found.

c. How do these two probabilities compare?

Answer #1

Topic: Poisson Probability Distribution
The Poisson Distribution is a discrete probability distribution
where the number of occurrences in one interval (time or area) is
independent of the number of occurrences in other intervals.
April Showers bring May Flowers!! Research the "Average Amount
of Days of Precipitation in April" for a city of your choice.
Introduce
Introduce the City and State. Let us know a fun fact!
Tell us the average number of days of precipitation in that
city for the...

A customer support center for a computer manufacturer receives
an average of 1.3 phone calls every five minutes. Assume the number
of calls received follows the Poisson distribution.
b. What is the probability that 3 or more calls will arrive
during the next five? minutes?
c. What is the probability that 3 calls will arrive during the
next ten? minutes?
d. What is the probability that no more than 2 calls will arrive
during the next ten? minutes?

Topic: Poisson Probability Distribution
The Poisson Distribution is a discrete probability distribution
where the number of occurrences in one interval (time or area) is
independent of the number of occurrences in other intervals. April
Showers bring May Flowers!! Research the "Average Amount of Days of
Precipitation in April" for a city of your choice. In your initial
post, Introduce Introduce the City and State. Let us know a fun
fact! Tell us the average number of days of precipitation in...

ind the indicated probabilities using the geometric?
distribution, the Poisson? distribution, or the binomial
distribution. Then determine if the events are unusual. If?
convenient, use the appropriate probability table or technology to
find the probabilities. A newspaper finds that the mean number of
typographical errors per page is nine. Find the probability that?
(a) exactly five typographical errors are found on a? page, (b) at
most five typographical errors are found on a? page, and? (c) more
than five typographical...

Find the indicated probabilities using the geometric
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Find the probability that the number of adults who say that they
have cheated on a test before is
(a) exactly
four,
(b) more than
two,
and...

Suppose that the time between successive occurrences of an event
follows an exponential distribution with mean number of occurrences
per minute given by λ = 5. Assume that an event occurs. (A) Derive
the probability that more than 2 minutes elapses before the
occurrence of the next event. Derive the probability that more than
4 minutes elapses before the occurrence of the next event. (B) Use
to previous results to show: Given that 2 minutes have already
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Find the indicated probabilities using the geometric
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convenient, use the appropriate probability table or technology to
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The mean number of births per minute in a country in a recent
year was about four.
Find the probability that the number of births in any given
minute is
(a) exactly
six,
(b) at least
six,
and (c) more than
six.

Find the indicated probabilities using the geometric
distribution, the Poisson distribution, or the binomial
distribution. Then determine if the events are unusual. If
convenient, use the appropriate probability table or technology to
find the probabilities. The mean number of births per minute in a
country in a recent year was about seven. Find the probability that
the number of births in any given minute is (a) exactly four (b)
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Every day, patients arrive at the dentist’s office. If the
Poisson distribution were applied to this process:
a.) What would be an appropriate random variable? What would be
the exponential-distribution counterpart to the random
variable?
b.)If the random discrete variable is Poisson distributed with λ
= 10 patients per hour, and the corresponding exponential
distribution has x = minutes until the next arrival, identify the
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1. P(x less than or equal to 6)...

One of the earliest applications of the Poisson distribution was
in analyzing incoming calls to a telephone switchboard. Analysts
generally believe that random phone calls are Poisson distributed.
Suppose phone calls to a switchboard arrive at an average rate of
2.2 calls per minute. (Round to 4 decimal places)
a. If an operator wants to take a one-minute
break, what is the probability that there will be no calls during a
one-minute interval?
b. If an operator can handle at...

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