The number of visits to a website follows a poisson distribution with an average of 90...

Question

Question

The number of visits to a website follows a poisson distribution with an average of 90 per hour.

What is the probability that there will be at least 2 visits in one minute?

What is the probability that the time between successive visits will be less than 0.5 minutes?

math Statistics-And-Probability

Answer 1

Answer #1

1)

expected number of visits in 1 minute =90/60 =1.5

probability that there will be at least 2 visits in one minute =P(X>=2)=1-P(X<=1)

=1-e^-1.5*1.5⁰/0!-e^-1.5*1.5¹/1! =1-0.557825 =0.442175

2) probability that the time between successive visits will be less than 0.5 minutes

=1-e^-1.5*0.5 =0.527633

Answer 2

Similar Homework Help Questions

The number of visits to a website is known to have a Poisson distribution with a...

The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute. a) What is the probability distribution for x, the number of visits per minute? p(X)=?? b) What is the probability that the number of visits per minute is less than or equal to 10? (Round your answer to three decimal places.) c) What is the probability that the number of visits per minute is greater than 14? (Round...
The number of hits to a web site follows a Poisson distribution. If the average number of...

The number of hits to a web site follows a Poisson distribution. If the average number of hits per minute is 6, answer the following questions: The probability of no hits in the next minute? The probability of exactly eight hits in the next minute? The probability of exactly eight hits in the next 2 minutes? The probability of at least 6 hits in the next 2 minutes? Expected number of hits in an hour?
If we assume the number of visits to a blog has a Poisson distribution, with average...

If we assume the number of visits to a blog has a Poisson distribution, with average of 99 visits per second. Let X be the waiting time until one visit to the blog: a) What distribution does X follow? State the probability density function of x and give an appropriate graphing rage of x for f(x) b) What is the probability that at least 50 seconds are needed until one visit occur?

The number of hits on a certain website follows a Poisson distribution with a mean rate...

The number of hits on a certain website follows a Poisson distribution with a mean rate of 4 per minute. What is the probability that 5 messages are received in a given minute?
The number of messages sent to a computer website is a Poisson random variable with a...

The number of messages sent to a computer website is a Poisson random variable with a mean of 5 messages per hour. a. What is the probability that 5 messages are received in 1 hours? b. What is the probability that fewer than 2 messages are received in 0.5 hour? c. Let Y be the random variable defined as the time between messages arriving to the computer bulletin board. What is the distribution of Y? What is the mean of...
Suppose that visits to a website can be modeled by a Poisson process with a rate λ=10 per hour (a...

suppose that visits to a website can be modeled by a Poisson process with a rate λ=10 per hour (a) What is the probability that there are more than or equal to 2 visits within a given 1/2 hour interval (b) A supervisor starts to monitor the website from the start of a new shift. then what is the expected value of time waited by the supervisor until the 10th visit to the website during that shift? Suppose that visits...

The number of customers that enter a bank follows a Poisson distribution with an average of...

The number of customers that enter a bank follows a Poisson distribution with an average of 30 customers per hour. What is the probability that exactly 3 customers would arrive during a 12 minute period?
The number of visitors to a webserver per minute follows a Poisson distribution. If the average...

The number of visitors to a webserver per minute follows a Poisson distribution. If the average number of visitors per minute is 4, what is the probability that: (i) There are two or fewer visitors in one minute? (2 points) (ii) There are exactly two visitors in 30 seconds? (2 points)
The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers...

The number of cars arriving at a gas station follows a Poisson distribution with μ=20 customers in an hour. Let X= waiting time (in minutes) between two arrivals. What is the distribution of X? What is the probability of having no arrivals in a 10-minute interval? What is the probability that the next arrival is within 5 minutes?

Suppose the number of emails sent from a system follows the Poisson distribution, which averages 30...

Suppose the number of emails sent from a system follows the Poisson distribution, which averages 30 times per hour. a. Find the probability that an email will not be sent for a certain minute. b. Let T be a random variable that represents the time between when an email is sent and the next email is sent., Find the probability distribution of T and use this to determine the probability of more than 10 minutes of time between when an...