Question

With an average of 2.5 per day following Poisson distribution, what is the probability that the...

With an average of 2.5 per day following Poisson distribution, what is the probability that the next day there is only 1?
What is the probability that there is at least 2 the next day?
What is the probability that there are at most 2 the next day?

Homework Answers

Answer #1

Let X ~ Poisson( = 2.5)

Then, P(X = x) = exp(-2.5) 2.5x / x!

Probability that the next day there is only 1 = P(X = 1)

= exp(-2.5) * 2.51 / 1!

= exp(-2.5) * 2.5

= 0.2052125

Probability that there is at least 2 the next day = P(X 2)

= 1 - P(X < 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [exp(-2.5) * 2.50 / 0! + exp(-2.5) * 2.51 / 1!]

= 1 -  [exp(-2.5) + exp(-2.5) * 2.5]

= 1 - (0.082085 + 0.2052125)

= 0.7127025

Probability that there is at most 2 the next day = P(X 2)

= P(X = 0) + P(X = 1) + P(X = 2)

= exp(-2.5) * 2.50 / 0! + exp(-2.5) * 2.51 / 1! + exp(-2.5) * 2.52 / 2!

= exp(-2.5) + exp(-2.5) * 2.5 + exp(-2.5) * 2.52 / 2

= 0.082085 + 0.2052125 + 0.2565156

= 0.5438131

= 0.7127025

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. Suppose the number of junk emails you received per day has a Poisson distribution with...
1. Suppose the number of junk emails you received per day has a Poisson distribution with an average of five per day. a) What is the probability that you receive 3 junk emails per day? b) What is the probability that you receive at least 1 junk email per day? c) What is the probability that you receive at most 3 junk emails per day? d) What is the likelihood of receiving between 3 and 6 junk emails per day?
The number of times a geyser erupts in one day follows a Poisson distribution with mean...
The number of times a geyser erupts in one day follows a Poisson distribution with mean 2.5. On a randomly selected day: (a) what is the probability that there are no eruptions? (b) what is the probability of at least 3 eruptions?
The number of customers that enter a Starbucks follows a Poisson distribution with an average of...
The number of customers that enter a Starbucks follows a Poisson distribution with an average of 2 customers every 15 minutes. (a) What is the probability that on the next hour at least six customers enter this Starbucks? (b) Assuming that a customer just walked in, what is the probability that the next customer walks in after 15 minutes? (c) Suppose 5% of people who pass this Starbucks enter for a coffee. What are the chances that among the next...
the average number of patients arriving at the emergency room is 10 per hour, what probability...
the average number of patients arriving at the emergency room is 10 per hour, what probability distribution should be used in order to find the probability that at least 8 patient will arrive within the next hour a-binomial b-poisson c-multinomial d-uniform e-geometric
Q2)   Consider a Poisson probability distribution with λ=4.9. Determine the following probabilities. ​a) exactly 5 occurrences...
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...
The following chart represents the probability distribution for the numbers of employees absent per day at...
The following chart represents the probability distribution for the numbers of employees absent per day at a medium-sized business. x( # of the employees absent) f(x) probability 0 0.3 1 0.2 2 0.1 3 0.3 4 0.1 1. What is the probability that at least 4 employees will be absent? 2. What is the probability that 1 or more employees will be absent? 3. What is the probability that fewer than 3 employees will be absent? 4. What is the...
Q: If you receive on average 2 spam emails per day, what is the probability that...
Q: If you receive on average 2 spam emails per day, what is the probability that you don't receive any spam email on a given day? Q: Given P(X)=0.2 P(X)=0.2, P(Y)=0.3 P(Y)=0.3 and P(X∩Y)=0.1 P(X∩Y)=0.1, what is P(X|Y)P(X|Y)? Q: What is the smallest possible sample mean of a bootstrap sample that you can obtain from the sample [1,2,3,4,5]? Q: An insurance company records on average 10 CTP claims per day. What is the probability that on a particular day at...
Every day, patients arrive at the dentist’s office. If the Poisson distribution were applied to this...
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 mean of x and determine the following: 1. P(x less than or equal to 6)...
Suppose that the number of Wi-fi interruptions in your home network follows the Poisson distribution with...
Suppose that the number of Wi-fi interruptions in your home network follows the Poisson distribution with an average of 1.5 per day. a. Calculate the probability that will have exactly 2 interruptions tomorrow. b. Calculate the probability that you will have at least 2 interruptions tomorrow.
Use the Poisson Distribution Formula to find the indicated probability. For a certain type of fabric,...
Use the Poisson Distribution Formula to find the indicated probability. For a certain type of fabric, the average number of defects in each square foot of fabric is 1.8. Find the probability that a randomly selected square foot of the fabric will contain at least two defects. Round your answer to four decimal places. Hint: The answer is the complement of the probability that there is at most 1 defect
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT