Question

In: Statistics and Probability

The number of complaints received by a company each month follows a Poisson distribution with mean...

The number of complaints received by a company each month follows a Poisson distribution
with mean 6.


(a) Calculate the probability the company receives no complaint in a certain week.
(b) Calculate the probability the company receives more than 4 complaints in a 2-week
period.
(c) Over a certain month, calculate the probability the company receives fewer complaints
than it usually does with respect to its monthly average.

Solutions

Expert Solution


Related Solutions

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?
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 calls that come into a small mail-order company follows a Poisson distribution. Currently,...
The number of calls that come into a small mail-order company follows a Poisson distribution. Currently, these calls are serviced by a single operator. The manager knows from past experience that an additional operator will be needed if the rate of calls exceeds 15 per hour. The manager observes that 6 calls came into the mail-order company during a randomly selected 15-minute period. a. If the rate of calls is actually 20 per hour, what is the probability that 9...
The number of calls that come into a small mail-order company follows a Poisson distribution. Currently,...
The number of calls that come into a small mail-order company follows a Poisson distribution. Currently, these calls are serviced by a single operator. The manager knows from past experience that an additional operator will be needed if the rate of calls exceeds 15 per hour. The manager observes that 6 calls came into the mail-order company during a randomly selected 15-minute period. a. If the rate of calls is actually 20 per hour, what is the probability that 9...
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...
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 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...
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 earthquakes that occur per week in California follows a Poisson distribution with a...
The number of earthquakes that occur per week in California follows a Poisson distribution with a mean of 1.5. (a) What is the probability that an earthquake occurs within the first week? Show by hand and provide the appropriate R code. (b) What is the expected amount of time until an earthquake occurs? (c) What is the standard deviation of the amount of time until two earthquakes occur? (d) What is the probability that it takes more than a month...
If student arrivals to the school dining commons follows the Poisson distribution with a mean of...
If student arrivals to the school dining commons follows the Poisson distribution with a mean of 50 students per day. For a randomly selected 36 days: (use 4 digits after decimal point) What is the probability that they served breakfast to at least 1757 students during these 36 days? [hint: P(ΣX ≥ 1757 students) =?]
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT