Before beginning work on this week’s discussion post, review the following resources:

• Doing Discussion Questions Right 
• Expanded Grading Rubric

From the below list, select one topic for which you will lead the discussion in the forum this week. Early in the week, reserve your selected topic by posting your response (reservation post) to the Discussion Area, identifying key words about your topic in the subject line.
By the due date assigned, research your topic and start a scholarly conversation as you respond with your initial or primary post to your own reservation post in the Discussion Area. Make sure your response does not duplicate your colleagues’ responses:
Topic:

• Evaluate the difference between simple and multiple linear regression techniques, including example business or research scenarios where you can apply them.

As the beginning of a scholarly conversation, your initial post should be:

• Succinct—no more than 500 words.
• Provocative—use concepts and combinations of concepts from the readings to propose relationships, causes, and/or consequences that inspire others to engage (inquire, learn). In other words, take a scholarly stand.
• Supported—scholarly conversations are more than opinions. Ideas, statements, and conclusions are supported by clear research and citations from course materials as well as other credible, peer-reviewed resources.

All posts must 100% original work. no plagiarism. Post results must be provided using Excel. Make sure you interpret your results on a Word Document.
Recall the car data set you identified in Forum 2 excel attached. We know that this data set is normally distributed using the mean and SD you calculated.  (Be sure you use the numbers without the supercar outlier)
For the next 4 cars that are sampled, what is the probability that the price will be less than $500 dollars below the mean?  Make sure you interpret your results.
Please note: we are given a new sample size, we will need to calculate a new SD.  Then, to find the value that is $500 below the mean you will need to take the mean and subtract $500 from it.  For example, if the mean is $15,000 then $500 below this would be $14,500.  Thus the probability you would want to find is P(x < 14,500).
For the next 4 cars that are sampled, what is the probability that the price will be higher than $1000 dollars above the mean?  Make sure you interpret your results.  Use the same logic as above.  If your mean is $15,000 then $1,000 above is 15,000 + 1,000 = $16,000.  Thus the probability you would want to find is P(x > 16,000).
For the next 4 cars that are sampled, what is the probability that the price will be equal to the mean?  Make sure you interpret your results.  Use the same logic as above.
For the next 4 cars that are sampled, what is the probability that the price will be $1500 within the mean?  Make sure you interpret your results.  Use the same logic as above.
I encourage you to review the Week 4 normal probabilities PDF at the bottom of the discussion.  This will give you a step by step example to follow and show you how to find probabilities using Excel.  I also encourage you to review the Week 4 Empirical Rule PDF.  This will give you a better understanding on how to utilize the empirical rule.

Provide (2) 200 words response with a minimum of 1 APA references for RESPONSES 1 AND 2 below. Responses may include direct questions. In your peer posts, compare the probabilities that you found with those of your classmates. Were they higher/lower and why? In your responses, refer to the specific data from your classmates’ posts. Make sure you include your data set in your initial post as well. Attached are the excel docs for both responses.
RESPONSE 1:
For this weeks forum I determined that my average price for the SUV’s that I selected was $49,903.60. Out of the 10 vehicles that I chose 6 of the cars were less than the average of all the cars price giving me a probability of p=.60 and a q=.40. When I calculated the probability of 10 randomly selected cars that exactly 4 of them will fall below my average I got 11%. When I calculated the probability that fewer than 5 of them would fall below the average I got slightly over 16%. Next, I calculated the probability that more than 6 of them would fall below my average and got 38%. What was interesting is that when I calculated the probability that at least 4 cars would fall below the average of my vehicles I got 94.5%. I think that this is a good exercise to learn in being able to speak to the likelihood that a car dealer will likely have the vehicle a customer is looking for based on the customer’s price point. If the dealer knows their averages they can also make suggestions and marketing assumptions that they have a good probability that a customer will find a vehicle of their choice within their price range using the information we covered in this weeks lesson. The formulas based on the pdf were explained at the bottom of the attached spreadsheet.
RESPONSE 2:
The average of my vehicles came out to $16,593. Half of the car’s prices fell below the average which made my probability success and failure 0.5. Both p=0.5 and q=0.5.
Average = $16,593
5 of my vehicles fall below the average
P= 5/10
P or Success = 0.5
Q = 1-p
Q = 1-0.5
Q or Failure = 0.5
In another random sample using the same data, the probability that exactly 4 cars would fall below the average is 21%.
In another random sample using the same data, the probability that fewer than 5 vehicles would fall below the average is 62%.
In another random sample using the same data, the probability that more than 6 vehicles will fall below the average is 17%.
In another random sample using the same data, the probability that at least 4 vehicles will fall below the average is 83%.
The results did not particularly surprise me. Since my probability was 0.5 is made it easier to simply look at the numbers and make a guess. The result that probably surprised me the most was how little the probability for exactly 4 vehicles falling below the average was. But then again, anytime you see the word “exactly” I would imagine a lower probability. Another extremely helpful pdf for this exercise. It was easy to follow and helped me understand the material more clearly.
Jenny