Question

The number of different mathematics courses at community colleges has a Poisson Distribution with a mean of 20 courses per college.

*show your basic keystrokes and round your answer to 4 decimal places.

- What is the probability there will be fewer than 38 courses at 2 colleges?

Someone on this site already answered this question, but I don't understand what they did, how they got the number 40 for this problem to solve it. Can you help me understand this please? I also didn't know if this was poissoncdf or poissonpdf.

Step 1

**The Poisson distribution:**

A discrete random variable *X *is said to have a Poisson distribution with parameter *λ* then the probability mass function (pmf) of the random variable is given by:

Step 2

**Additive property of two independent Poisson random variable:**

If two independent random variables *X*_{1} and *X*_{2} follow a Poisson distribution with parameter(mean) λ_{1 }and λ_{2} respectively then their sum also follow a Poisson distribution with parameter λ_{1 }+ λ_{2}. That is, *X *follows P (λ_{1}) and *Y *follows P (λ_{2}) then *X*_{1}*+ X*_{2} follows P (λ_{1 }+ λ_{2}).

Step 3

**Calculation:**

The number of different mathematics courses at community college has a Poisson distribution with mean 20 courses per college. For Poisson distribution mean is same as the parameter. The random variable *X*1 denote number of different mathematics courses at first community college. The random variable *X*2 denote number of different mathematics courses at second community college. It is known that number of different mathematics courses at community college has a Poisson distribution with mean (parameter) 20 courses per college. The random variables *X*1 and *X*2 are independent also. Therefore, each random variable *X*1 and *X*2 follows Poisson distri...

Tagged in

Q: An advertising executive wants to determine if a new billboard placed in a city caused sales of thei...

A: Given that we need to test to determine if a new billboard played in a city caused sales of their pr...

Q: Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and...

A: Let r denote the linear correlation between advertising cost (x) and profit (y). The hypotheses are ...

Q: 2. Previously, you studied linear combinations of independent random variables. What happens if the ...

A: Consider the provided information:μx ≈ 7.34, σx ≈ 6.55, μy ≈ 13.19, σy ≈ 18.57, ...

Q: List and describe two of the common types of explanations for statistical relationships (other than ...

A: Common types of explanations for statistical relationships:The common types of explanations for stat...

Q: Consider a drug that is used to help prevent blood clots in certain patients. In clinical trials, am...

A: Test statistic calculation:The test hypotheses are:Null hypothesis:H0: p = 0.03, that is, 3% in the ...

Q: A recent poll by the American Automobile Club found that 74.5% of those surveyed are worried about a...

A: Hey there! Thank you for posting the question. As your question has more than 3 parts, we have solve...

Q: entle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the...

A: (a) Level of significance:Level of significance (α) indicates the probability of rejecting null hyp...

Q: BASED ON THIS DATA, what does the r^2 values tell you? and the linear regression line is the inform...

A: Note:Hi there! Thank you for posting the question! However, the circumstances of the study presented...

Q: It is thought that prehistoric Indians did not take their best tools, pottery, and household items w...

A: Given data obtained for a collection of archeological sites in New Mexico as shown below. The least ...

Sorry about that. What wasn’t helpful?