Customers arrive at a restaurant at a random rate of 9 per hour. What the probability that during any 120 minute period, the number of customers arriving at the restaurant is exactly 6. What type of a distribution is this?Question 3Select one:a.Poisson distributionb.Exponential distributionc.Uniform distributiond.Binomial distribution
Question
Customers arrive at a restaurant at a random rate of 9 per hour. What the probability that during any 120 minute period, the number of customers arriving at the restaurant is exactly 6. What type of a distribution is this?Question 3Select one:a.Poisson distributionb.Exponential distributionc.Uniform distributiond.Binomial distribution
Solution
This is a Poisson distribution problem. The Poisson distribution is used to model the number of events occurring within a given time interval. The formula for the Poisson probability is:
P(x; μ) = (e^-μ) * (μ^x) / x!
where:
- P(x; μ) is the Poisson probability,
- e is the base of the natural logarithm (approximately equal to 2.71828),
- μ is the average rate of value,
- x is the actual number of successes that result from the experiment.
Here, the rate of customers arriving is 9 per hour. So, for a 120 minute (or 2 hour) period, the rate would be 9 * 2 = 18 customers.
We want to find the probability that exactly 6 customers arrive in this period. So, we substitute these values into the formula:
P(6; 18) = (e^-18) * (18^6) / 6!
Calculate this value to get the probability.
So, the answer to the question "What type of a distribution is this?" is a. Poisson distribution.
Similar Questions
Customers arrive at a restaurant at a random rate of 9 per hour. What the probability that during any 120 minute period, the number of customers arriving at the restaurant is exactly 6.Question 22Select one:a.0.1171b.0.0255c.0.0437d.0.0025
At a dress shop, it is noticed that 120 people are arriving in 2 hours. Given this what is the probability that, during 1 minute period, exactly 5 people arrive. Use Poisson Distribution and round your answer to four decimal places.
The food court at an amusement park has an ice cream shop. The shop has 17 customers arrive over 85 minutes.Use the Poisson distribution to find the probability that the shop has more than 1 arrival in a given minute.Do not round intermediate computations, and round your answer to three decimal places.(If necessary, consult a list of formulas.)
A park receives an average of 20 tourists per hour. Assuming that the arrival time of tourists follows a Poisson distribution, what is the probability that exactly 8 tourists will be received in any given hour?Round your results to four decimal places.
On an average, a clothing store gets 120 customers per day. Let the random variable be X~P (120). What is the probability of getting 150 customers in one day?Question 4Answera.0.05b.0.0010c.0.2
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.