Question

In: Statistics and Probability

A website manager has noticed that during the evening hours, about 3 people per minute check...

A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of others and assumes that the distribution of number of purchases per minute on the website follows Poisson distribution.

  1. What is the probability that during a 1-minute period, at least one purchase is made?

  2. What is the probability that no one makes a purchase in next 2 minutes?

  3. What is the probability that no more than 5 people will make a purchase in next three

    minutes?

Solutions

Expert Solution

Let , X : Number of people check out from their shopping cart and make an online purchase.

Since , A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase.

And PMF of Poisson distribution is given by

   , x = 0 ,1,2,3,... , m >0

The probability that during a 1-minute period, at least one purchase is made is given by ,

Therefore , Probability that during a 1 minutes period , at least one purchase is made is 0.9502 .

The probability that no one makes a purchase in next 2 minutes is given by ,

Let ,

For first one minute , X = Number of people check out from their shopping cart and make an online purchase in first one minute.

For second minute , Y =Number of people check out from their shopping cart and make an online purchase in second minute .

Since X & Y are independent .

Therefore , Probability that no one makes a purchase in next 2 minute is given by ,

The probability that no more than 5 will  make a purchase in next 3 minutes is given by ,

Let ,

For first one minute , X = Number of people check out from their shopping cart and make an online purchase in first one minute.

For second minute , Y =Number of people check out from their shopping cart and make an online purchase in second minute .

For third minute , Z=Number of people check out from their shopping cart and make an online purchase in third minute .

.

Since X , Y , Z are independent .

The probability that no more than 5 will  make a purchase in next 3 minutes is given by

Therefore by using pmf

The probability that no more than 5 will  make a purchase in next 3 minutes is given by ,

The probability that no more than 5 will  make a purchase in next 3 minutes is = 0.1157

orchestra answered 1 year ago
Next > < Previous

Related Solutions

An airline maintenance manager has a bright idea. He has noticed that many “C” check write-ups...
An airline maintenance manager has a bright idea. He has noticed that many “C” check write-ups are generated from leaky and loose components in the aircraft’s ground spoiler system. He suspects that by deactivating these ground spoilers, he can save money on “C” checks without appreciably effecting ground roll distances on landing. He thinks that reverse thrust and braking alone will be more than enough, and the ground spoilers are not necessary. He tested his theory by deactivating the ground...
The number of people entering a security check-in lineup in a 15-minute interval at a medium...
The number of people entering a security check-in lineup in a 15-minute interval at a medium sized airport can be modeled by the following probability model: ?(?=?)=?−16.6(16.6)??!?=0,1,2,⋯P(X=x)=e−16.6(16.6)xx!x=0,1,2,⋯ Part (a) What does 16.6 represent in the probability model? Select the most appropriate explanation below. A. 16.6 represents how much skewed the distribution of values is. B. 16.6 represents a weighted-average of the number of people who enter the a security check-in lineup every 15-minutes. C. 16.6 is the rate at which...
A production manager at a pottery factory has noticed that about 70 percent of defects result...
A production manager at a pottery factory has noticed that about 70 percent of defects result from impurities in raw materials, 15 percent result from human error, 10 percent from machine malfunctions, and 5 percent from a variety of other causes. This manager is most likely using a-Select one:a. cause-and-effect diagram.b. scatter diagram.c. quality loss function.d. Pareto chart.e. flowchart.
Janitors per evening 0 1 2 3 4 5 6 7 Classrooms cleaned per evening 0...
Janitors per evening 0 1 2 3 4 5 6 7 Classrooms cleaned per evening 0 3 7 12 16 17 17 16 1. What is the marginal product of the second janitor? 2. What is the average product of four janitors? 3. Is the addition of the 3rd, 4th and 7th janitor associated with increasing, diminishing, or negative marginal returns? Explain. 4. Draw the total product, average product, and marginal product curves and shade the regions corresponding to increasing...
A particular professor has noticed that the number of people, P, who complain about his attitude...
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 12 10 10 7 6 6 3 Cups of coffee (n) 1 1 2 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. a) Using regression to find a linear equation for...
A particular professor has noticed that the number of people, P, who complain about his attitude...
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 11 12 10 9 6 6 6 4 Cups of coffee (n) 1 1 2 2 3 3 4 5 Unless otherwise stated, you can round values to two decimal places. Parts d), e) and g) will not be graded...
A particular professor has noticed that the number of people, P, who complain about his attitude...
A particular professor has noticed that the number of people, P, who complain about his attitude is dependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiled the following data: People (P) 10 11 9 9 8 6 7 5 Cups of coffee (n) 1 1 2 2 3 4 4 5 Unless otherwise stated, you can round values to two decimal places. a) Using regression to find a linear equation for...
MALDEN MILLS CASE STUDY During the early evening hours of December 11, 1995, a fire broke...
MALDEN MILLS CASE STUDY During the early evening hours of December 11, 1995, a fire broke out in a textile mill in Lawrence, Massachusetts. By morning, the fire had destroyed most of Malden Mills, the manufacturer of Polartec fabric. The fire seemed a disaster to the company, its employees, its customers, and the surrounding communities. Malden Mills was a family-owned business, founded in 1906 and run by the founder’s grandson, Aaron Feuerstein. Polartec is a high-quality fabric well known for...
A researcher has obtained the number of hours worked per week during the summer for a...
A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. 40 25 35 30 20 40 30 20 40 10 30 20 10 5 20 Using this data set, compute the a. Median and mode b. mean c. 40th percentile d. range e. sample variance f. standard deviation
Cutting Speed (meters per minute) Useful Life Brand A (Hours) Useful Life Brand B (Hours) 30...
Cutting Speed (meters per minute) Useful Life Brand A (Hours) Useful Life Brand B (Hours) 30 5.2 6.3 30 4.4 6.4 30 5.2 5.2 40 4.5 6.0 40 3.7 4.6 40 2.5 5.0 50 4.4 4.5 50 2.8 4.0 50 1.0 3.7 60 4.0 3.8 60 2.0 3.0 60 1.1 2.4 70 1.1 1.5 70 0.5 2.0 70 3.0 1.0 . Use a 95​% confidence interval to estimate the mean useful life of a brand A cutting tool when the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT