probabilities responses
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
Car Analysis
| Vehicle Ty | p | Year | Make | Mode | Price | MPG (city) | MPG (Highway) | Horsepower | |||||||||||||||||
| SUV | 20 | Toyota | 4Runner | $ 45,012.00 | 16 | 19 | 27 | ||||||||||||||||||
| 2021 | Chevrolet | Tahoe | $ 60,030.00 | 355 | |||||||||||||||||||||
| 2020 | Land Rover | Range | $ 93,775.00 | 18 | 23 | ||||||||||||||||||||
| Rav4 Prime | $ 31, | 228 | 41 | 38 | 219 | ||||||||||||||||||||
| Suburban | $ 71,445.00 | 15 | |||||||||||||||||||||||
| Genesis | GV80 | $ 60,620.00 | 37 | ||||||||||||||||||||||
| Lexus | UX | $ | 29 | 169 | |||||||||||||||||||||
| Audi | Q3 | $ 29,688.00 | |||||||||||||||||||||||
| Kia | Telluride | $ 44,343.00 | 26 | 291 | |||||||||||||||||||||
| Hyundai | Palisade | $ 32,995.00 | |||||||||||||||||||||||
| Supercar | McLaren | F1 | $ 19,800,000.00 | 24 | 600 | ||||||||||||||||||||
| Qualitative | Quantitative | ||||||||||||||||||||||||
| Average Price: | $ 49,903.60 | p=6/ | 10 | q | |||||||||||||||||||||
| 0.6 | |||||||||||||||||||||||||
| 0.4 | |||||||||||||||||||||||||
| P(x=4) | 11 | % of 10 Random Samples of Cars probability that exactly 4 of them will fall below the average | |||||||||||||||||||||||
| P(x<5) and P(x<=4) | 16.62% | % of 10 Random Samples of Cars probability that fewer than 5 of them will fall below the average | |||||||||||||||||||||||
| P(x>6) = 1 – P(x<=6)= 1 - P(x<=6) | 38.23% | % of 10 Random Samples of Cars probability that more than 6 of them will fall below the average | |||||||||||||||||||||||
| P(x>=4) = 1 – P(x<=4-1) = 1 - P(x<=3) | 94.52% | % of 10 Random Samples of Cars probability that at least 4 of them will fall below the average |
10 Vehicles
| Column1 | |||
| Mean | 49903.6 | ||
| Standard Error | 6753.1541325352 | ||
| Median | 44677.5 | ||
| ERROR:#N/A | |||
| Standard Deviation | 21355.34844899 | ||
| Sample Variance | 456050907.377778 | ||
| Kurtosis | 0.35728503 | ||
| Skewness | 0.9811742596 | ||
| 64087 | |||
| Minimum | 29688 | ||
| Maximum | 93775 | ||
| Sum | 499036 | ||
| Count |
11 Vehicles
| 1845366.90909091 |
| 1795473.70004346 |
| 45012 |
| 5954912.58399526 |
| 35460983883025.1 |
| 10.9996604096 |
| 3.3165544515 |
| 19770312 |
| 19800000 |
| 20299036 |
car stats
with addition
| Price | ||||||||||||||||||||||||
| Mean | 187812 | |||||||||||||||||||||||
| Standard Error | 17 | 6 | 30 | 25 | ||||||||||||||||||||
| Median | 17230 | |||||||||||||||||||||||
| Mode | ERROR:#N/A | |||||||||||||||||||||||
| Standard Deviation | 567877.879569895 | |||||||||||||||||||||||
| Sample Variance | 322 | 4 | 28 | 10 | ||||||||||||||||||||
| Kurtosis | 10.99903 | 27 | ||||||||||||||||||||||
| Skewness | 3.3164 | 24 | 26 | |||||||||||||||||||||
| Range | 1889582 | |||||||||||||||||||||||
| Minimum | 10418 | |||||||||||||||||||||||
| Maximum | 1900000 | |||||||||||||||||||||||
| Sum | 2065932 | |||||||||||||||||||||||
| Count | 11 | |||||||||||||||||||||||
| Confidence Level(95.0%) | 38 | 34 |
car stats
| 16593.2 | ||||
| 1086.9885494644 | ||||
| 16587.5 | ||||
| 3437. | 35 | |||
| 11815441.0666667 | ||||
| 0.0413190783 | ||||
| -0.11375321 | ||||
| 115 | 33 | |||
| 21951 | ||||
| 165932 | ||||
| 2458.9389330505 |
Car information
| Vehicle type | Year | Make | Model | MPG (city) | MPG (highway) | Cylinders | |||||||||||||||
| Sedan | 2018 | Ford | Focus | $10,418 | |||||||||||||||||
| Utility | 2017 | Nissan | Rogue | $13,405 | |||||||||||||||||
| Subaru | Legacy | $14,385 | Average | $16,593 | |||||||||||||||||
| Honda | HR-V | $15,819 | P=5/10 | 0.5 | |||||||||||||||||
| 2019 | Hyundai | Sonata | $15,945 | q=1-0.5 | |||||||||||||||||
| 2016 | Cadillac | SRX | $17,230 | ||||||||||||||||||
| Accord | $17,805 | ||||||||||||||||||||
| Toyota | Camry | $17,935 | 39 | ||||||||||||||||||
| Crosstrek | $21,039 | ||||||||||||||||||||
| RAV4 | $21,951 | ||||||||||||||||||||
| qualitative | quantitative |
Probabilities
| $16,695 | ||
| P(X=4) | 0.205078125 | 21% |
| P(X≤5) | 0.62304688 | 62% |
| 1-P(X≤3) | 0.828125 | 83% |
| 1-P(X≤6) | 0.171875 | 17% |