1 Answer

Ask a Question

Pistal · Answer 1 · 2022-04-19T19:42:21+0000

Answer:

1. c. Poisson

2. 0.9592 = 95.92% probability that in any one minute at least one purchase is made.

3. 0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.

Explanation:

We have only the mean, which means that the Poisson distribution is used to solve this question, and thus the answer to question 1 is given by option c.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Mean of 3.2 minutes:

This means that
$\mu = 3.2n$ , in which n is the number of minutes.

2. What is the probability that in any one minute at least one purchase is made?

n = 1 , so
$\mu = 3.2$ .

This probability is:

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

P(X = 0) = (e^(-3.2)*3.2^(0))/((0)!) = 0.0408

So

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0408 = 0.9592$

0.9592 = 95.92% probability that in any one minute at least one purchase is made.

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

2 minutes, so
$n = 2, \mu = 3.2(2) = 6.4$

This probability is P(X = 0). So

$P(X = x) = (e^(-\mu)*\mu^(x))/((x)!)$

P(X = 0) = (e^(-6.4)*6.4^(0))/((0)!) = 0.0017

0.0017 = 0.17% probability that no one makes a purchase in the next 2 minutes.

0 Comments

Please log in or register to add a comment.

Please log in or register to answer this question.

1 Answer

0 Comments

Please log in or register to add a comment.

Other Questions