Question

In: Statistics and Probability

The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate...

The cell number of a senator was published on Twitter. Following a Poisson distribution, the rate at which calls were coming through was 1.5 per minute.

a. What is the probability that no call came through in a one-minute period?

b. What is the probability that less than 180 calls came through in a two-hour period?

Solutions

Expert Solution

The poisson distribution have probability as , where the mean is lambda. The mean rate of calls is 1.5/min, and hence, the probability would be , for probability of x calls coming in a minute.

(a) The probability that zero calls came through in a minute will be or . Hence, there is a 22.313% chance that no call came in a minute.

(b) The average rate of calls is 1.5 per minute, and hence in two hours or 120 mins, the mean rate would be 1.5*120=180 calls per 2 hour. Probability of x calls coming in 2 hours is .

The probability that less than 180 calls came in those 2 hours is or . It can be calculated only by the help of any online calculator or via r, excel. I have used an online calculator, with the parameters x=180 and lambda=180, and we have . Hence, there are 49.01% chances of occuring that.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 9 people per hour. a) What is the probability that exactly 7 patients will arrive during the next hour? b. What is the probability that at least 7 patients will arrive during the next hour? c. How many people do you expect to arrive in the next two hours? d. One in four patients who come to the emergency room in hospital. Calculate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate...
The number of people arriving at an emergency room follows a Poisson distribution with a rate of 7 people per hour. a. What is the probability that exactly 5 patients will arrive during the next hour? (3pts) b. What is the probability that at least 5 patients will arrive during the next hour? (5pts) c. How many people do you expect to arrive in the next two hours? (4pts) d. One in four patients who come to the emergency room...
The number of arriving customers to a big supermarket is following a Poisson distribution with a...
The number of arriving customers to a big supermarket is following a Poisson distribution with a rate of 4 customers per a minute. What is the probability that no customer will arrive in a given minute? What is the probability that exactly 3 customers will arrive in a given minute? What is the probability that at least seven customer will arrive in a given minute? What is the probability that at most one customer will arrive in 40 seconds? What...
The number of imperfections in an object has a Poisson distribution with a mean λ =...
The number of imperfections in an object has a Poisson distribution with a mean λ = 8.5. If the number of imperfections is 4 or less, the object is called "top quality." If the number of imperfections is between 5 and 8 inclusive, the object is called "good quality." If the number of imperfections is between 9 and 12 inclusive, the object is called "normal quality." If the number of imperfections is 13 or more, the object is called "bad...
The number of views of a page on a Web site follows a Poisson distribution with...
The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. (i) What is the probability of no views in a minute? (ii) What is the probability of two or fewer views in 10 minutes? (iii) What is the probability of two or fewer views in 2 hours?
The number of airplane landings at a small airport follows a Poisson distribution with a mean...
The number of airplane landings at a small airport follows a Poisson distribution with a mean rate of 3 landings every hour. 4.1 (6%) Compute the probability that 3 airplanes arrive in a given hour? 4.2 (7%) What is the probability that 8 airplanes arrive in three hours? 4.3 (7%) What is the probability that more than 3 airplanes arrive in a period of two hours?
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an...
Suppose the number of earthquakes occurring in an area approximately follows a Poisson distribution with an average rate of 2 earthquakes every year. a.) Find the probability that there will be 1 to 3 (inclusive) earthquakes during the next year in this area. b.) Find the probability that there will be exactly 5 earthquakes during the next 3 year period. c.) Consider 10 randomly selected years during last century. What is the probability that there will be at least 3...
Suppose that Y is the Poisson distribution of the number of students a school has. Find...
Suppose that Y is the Poisson distribution of the number of students a school has. Find the mode by studying the monotonicity and explaining if the mean is a)5.3 and other case b) 6
The number of people crossing at a certain traffic light follows a Poisson distribution with a...
The number of people crossing at a certain traffic light follows a Poisson distribution with a mean of 6 people per hour. An investigator is planning to count the number of people crossing the light between 8pm and 10pm on a randomly selected 192 days. Let Y be the average of the numbers of people to be recorded by the investigator. What is the value of E[Y ]? A. 6 B. 12 C. 1152 D. 0.03125. What is the value...
Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆.
Assume that the number of defects in a car has a Poisson distribution with parameter 𝜆. To estimate 𝜆 we obtain the random sample 𝑋1,𝑋2, … , 𝑋n.a. Find the Fisher information is a single observation using two methods.b. Find the Cramer-Rao lower bound for the variance of an unbiased estimator of 𝜆.c. Find the MLE of 𝜆 and show that the MLE is an efficient estimator.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT