Question

Suppose that the time between arrivals of customers at a bank during the noon-to-1 p.m. hour has a uniform distribution between 0 and 30 seconds. a. What is the probability that the time between the arrivals of two customers will be less than 14 seconds? b. What is the probability that the time between the arrivals of two customers will be between 11 and 19 seconds? c. What is the probability that the time between the arrivals of two customers will be greater than 23 seconds? d. What are the mean and standard deviation of the time between the arrival of two customers?

Answer #1

4. Suppose that customers arrive at a bank according to a P P(λ)
with λ = 12 per hour. Compute the following: (a) The mean and
variance of the customers who enter the bank during 5 hours. (b)
Probability that more than 5 customers enter the bank during an
hour. (c) Probability that exactly 1 arrival between 9:00am and
11:00am and exactly 2 arrivals between 10:00am and 12:00 noon.

A busy restaurant determined that between 6:30 P.M. and 9:00
P.M. on Friday nights, the arrivals of customers are Poisson
distributed with an average arrival rate of 4.32 per minute.
*(Round your answer to 2 decimal places.) **(Round your answer to 4
decimal places.)
(a) What is the probability that at least 11 minutes will elapse
between arrivals?
(b) What is the probability that at least 4 minutes will elapse
between arrivals?
(c) What is the probability that at least...

The time (in minutes) between arrivals of customers to a post
office is to be modelled by the Exponential distribution with mean
0.38.
Please give your answers to two decimal places. Given that the
time between consecutive customers arriving is greater than ten
seconds, what is the chance that it is greater than fifteen
seconds

7. A store is expecting n deliveries between the hours
of noon and 1 p.m. Suppose the arrival time of each delivery truck
is uniformly distributed on this 1-hour interval and that the times
are independent of one another.
a) What percentage of the time the latest delivery arrives after
12:50?
b) What percentage of the time the first delivery arrives before
12:10?

The time between arrivals of vehicles at a particular
intersection follows an exponential probability distribution with a
mean of 10 seconds. (a) Sketch this exponential probability
distribution.
(b) What is the probability that the arrival time between
vehicles is 10 seconds or less? (Round your answer to four decimal
places.)
(c) What is the probability that the arrival time between
vehicles is 4 seconds or less? (Round your answer to four decimal
places.)
(d) What is the probability of 30...

Arrivals at a bank are Poisson distributed with a mean arrival
rate of two arrivals every five minutes.
a) What is the probability of exactly two arrivals in the next
four minutes?
b) Assuming that the previous arrival came to the bank 10
minutes ago (with no arrivals since then), what is the probability
that the time to next arrival will be greater than 1 minute?

The time between arrivals at a toll booth follows an
exponential distribution with a mean time between arrivals of 2
minutes.
What is the probability that the time between two successive
arrivals will be less than 3 minutes?
What is the probability that the time will be between 3 and 1
minutes?

Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
Find the probability of more than 25 people arriving within the
next two hours using the Poisson mass function.
Find the probability of more than 25 people arriving within the
next two hours using the normal approximation to the Poisson.
Compute the percent relative difference between the exact
probability computed in part 1 and...

Suppose that customers arrive at a bank at a rate of 10 per
hour. Assume that the number of customer arrivals X follows a
Poisson distribution.
1. Find the probability of more than 25 people arriving within
the next two hours using the Poisson mass function.
2. Find the probability of more than 25 people arriving within
the next two hours using the normal approximation to the
Poisson.
3. Compute the percent relative difference between the exact
probability computed in...

1. A restaurant serves an average of 180
customers per hour during the lunch time.
(a). What probability distribution is most
appropriate for calculating the probability of a given number of
customers arriving within one hour during lunch time?
(b). What are the mean and the standard
deviation of the number of customers this restaurant serves in one
hour during lunch time?
(c). Would it be considered unusually low if
only 150 customers showed up to this restaurant in one...

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