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.

What is the probability that during a 1-minute period, at least one purchase is made?
What is the probability that no one makes a purchase in next 2 minutes?
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

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