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In: Statistics and Probability

A website for a small motel chain averages seven visitors every ten minutes.   Solve the probability...

A website for a small motel chain averages seven visitors every ten minutes.   Solve the probability questions for Scenario 5 by hand. (Round all probabilities to 4 decimals)

What is the mean number of visitors in a 3-minute period?

What is the probability of no visitors in a 3-minute period?

What is the probability of exactly one visitor in a 3-minute period?

What is the probability of exactly two visitors in a 3-minute period?

What is the probability of three or more visitors in a 3-minute period?

What is the expected number of visitors to the website in six minutes?

What is the variance of the number of expected visitors to the website in six minutes?

What is the standard deviation of the number of expected visitors to the website in six minutes? (Round to two decimals

Solutions

Expert Solution

Solution:

What is the mean number of visitors in a 3-minute period?

Answer:

What is the probability of no visitors in a 3-minute period?

Answer: Let x be the number of visitors in a 3-minute period. Then we have to find:

Using the Poisson distribution probability function:

What is the probability of exactly one visitor in a 3-minute period?

Answer: It is required to find:

Using the Poisson distribution probability function:

What is the probability of exactly two visitors in a 3-minute period?

Answer:

It is required to find:

Using the Poisson distribution probability function:

What is the probability of three or more visitors in a 3-minute period?

Answer: It is required to find:

We know that:

Now using the answers of part b to part d, we have:

  

What is the expected number of visitors to the website in six minutes?

Answer: The expected number of visitors to the website in six minutes is:

What is the variance of the number of expected visitors to the website in six minutes?

Answer: The variance of the number of expected visitors to the website in six minutes is:

What is the standard deviation of the number of expected visitors to the website in six minutes?

Answer: The standard deviation of the number of expected visitors to the website in six minutes is:

orchestra answered 2 years ago
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