# The normal distribution I and II Responses

Open Posted By: ahmad8858 Date: 31/12/2020 High School Rewriting & Paraphrasing

Provide (2) 150 words response 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 to help with the post.

RESPONSE 1:

This week we worked with averages, standard deviations, and especialy probabilities.

The first step was to calculate a new standard deviation for a sample size of 4. In my case 14264/SQRT(4).

With this number and the previously calculated mean price of a vehicle, in my example 28232, we first calculate the percent chance that the next four vehicles will be 500 dollars below the mean. I came to a 47.2% chance.

The next probability we calculate is the odds of the next four cars being 1000 dollars above the mean. I came to a 44.4% chance this would be the case.

After that we calculate the odds that the next four cars would cost the same as my mean price. I came to a 50% chance that that would happen.

The final probability to calculate was if the next four cars would cost within 1500 dollars +- of the mean price. I came to a 16.7% chance that would happen.

Speaking for myself I found this post quite challenging and would welcome any critical eyes on work.

RESPONSE 2:

For this week's forum we are asked to find the normal distribution of a set of vehicles and different probabilities.

The mean of all my vehicles without the supercar is 18,478 and I have a new standard deviation of 685.3123781.

The first question asks for the probability that the price will be less than \$500 dollars below the mean. To figure this out we take my mean and subtract 500 dollars to get 17978. That is p(x<17978). In excel make sure to use norm.dist with a formula of TRUE.

Secondly we are asked to find the probability that the price will be higher than \$1000 dollars above the mean. To figure this out we take the mean and add 1000 dollars to get 19478. That is p(x>19478). In excel make sure to use norm.dist with a formula of TRUE.

Next we are asked to find the probability that the price will be equal to the mean. To figure this out we take the mean and equal it out against itself at 18478. That is p(x=18478). In excel make sure to use norm.dist with a formula of FALSE.

Finally we are asked to find the probability that the price will be \$1500 within the mean. To figure this out we take the mean 18478, and subtract 1500 as well as add 1500 in a separate equation. Within excel I input the normal distribution formula with the inputed numbers of =NORM.DIST(19978,16978,C28,TRUE)-NORM.DIST(16978,18478,C28,TRUE).

Category: Accounting & Finance Subjects: Behavioral Finance Deadline: 24 Hours Budget: \$80 - \$120 Pages: 2-3 Pages (Short Assignment)

## Sheet5

 Price Mean 216798.181818182 Standard Error 198320.569334179 Median 18610 Mode ERROR:#N/A Standard Deviation 657754.916691136 Sample Variance 432641530431.364 Kurtosis 10.9998853724 Skewness 3.3166010247 Range 2183730 Minimum 16270 Maximum 2200000 Sum 2384780 Count 11 Confidence Level(95.0%) 441885.765681523

## List

 Vehicle Year Make Model Price MPG City MPG Highway Fuel Capacity (Gallons) WAGON 2021 KIA SOUL \$18,610.00 25 31 14.3 w/o supercar SUV 2021 CHEVROLET TRAILBLAZER \$19,995.00 28 31 13.2 Mean 18478 Standard Error 433.4296046906 HATCHBACK 2020 HONDA FIT \$17,145.00 29 36 10.6 Median 18550 Mode ERROR:#N/A SUV 2021 HYUNDAI VENUE \$18,490.00 27 35 11.9 Standard Deviation 1370.6247561686 Sample Variance 1878612.22222222 SEDAN 2019 HYUNDAI ELANTRA \$18,130.00 26 36 14 Kurtosis -1.3456954168 Skewness -0.4165890254 SUV 2019 NISSAN KICKS \$19,735.00 31 36 10.8 Range 3725 Minimum 16270 COUPE 2020 HYUNDAI VELOSTER \$19,775.00 25 33 13.2 Maximum 19995 Sum 184780 SEDAN 2020 VOLKSWAGEN JETTA \$19,815.00 30 40 13.2 Count 10 Confidence Level(95.0%) 980.4858848196 SEDAN 2020 HYUNDAI ACCENT \$16,270.00 29 39 11.9 SEDAN 2020 KIA RIO \$16,815.00 33 41 11.9 w/ supercar SPORT 2016 Ferrari LaFerrari Aperta \$2,200,000.00 12 15 25 Mean 216798.181818182 Standard Error 198320.569334179 Qualitative Quantitative Qualitative Qualitative Quantitative Quantitative Quantitative Quantitative Median 18610 Mode ERROR:#N/A Mean: \$18,478.00 average price \$18,478.00 p(x=4) 20.01% exactly 4 Standard Deviation 657754.916691136 w/o supercar Median: \$18,550.00 under average 3 p(x<5) & p(x<=4) 84.97% fewer than 5 Sample Variance 432641530431.364 SD: 1370.6247561686 p=3/10=.30 p(x>6) = 1 - p(x<=6)= 1 - p(x<=6) 1.06% more than 6 Kurtosis 10.9998853724 Sample Size: 10 q=1-.30=.70 p(x>=4) = 1 - p(x<=4-1) = 1 - p(x<=3) 35.04% at least 4 Skewness 3.3166010247 p= 0.30 Range 2183730 Mean: \$216,798.18 q= 0.70 Minimum 16270 w/ supercar Median: \$18,610.00 Maximum 2200000 SD: 657754.916691136 Sum 2384780 Sample Size: 11 Count 11 Confidence Level(95.0%) 441885.765681523

## Normal Distribution

 Vehicle Year Make Model Price MPG City MPG Highway Fuel Capacity (Gallons) WAGON 2021 KIA SOUL \$18,610.00 25 31 14.3 w/o supercar SUV 2021 CHEVROLET TRAILBLAZER \$19,995.00 28 31 13.2 Mean 18478 Standard Error 433.4296046906 HATCHBACK 2020 HONDA FIT \$17,145.00 29 36 10.6 Median 18550 Mode ERROR:#N/A SUV 2021 HYUNDAI VENUE \$18,490.00 27 35 11.9 Standard Deviation 1370.6247561686 Sample Variance 1878612.22222222 SEDAN 2019 HYUNDAI ELANTRA \$18,130.00 26 36 14 Kurtosis -1.3456954168 Skewness -0.4165890254 SUV 2019 NISSAN KICKS \$19,735.00 31 36 10.8 Range 3725 Minimum 16270 COUPE 2020 HYUNDAI VELOSTER \$19,775.00 25 33 13.2 Maximum 19995 Sum 184780 SEDAN 2020 VOLKSWAGEN JETTA \$19,815.00 30 40 13.2 Count 10 Confidence Level(95.0%) 980.4858848196 SEDAN 2020 HYUNDAI ACCENT \$16,270.00 29 39 11.9 SEDAN 2020 KIA RIO \$16,815.00 33 41 11.9 w/ supercar SPORT 2016 Ferrari LaFerrari Aperta \$2,200,000.00 12 15 25 Mean 216798.181818182 Standard Error 198320.569334179 Qualitative Quantitative Qualitative Qualitative Quantitative Quantitative Quantitative Quantitative Median 18610 Mode ERROR:#N/A Mean: \$18,478.00 p(x<17978) 23.28% Standard Deviation 657754.916691136 SD: 1370.6247561686 p(x>19478) 7.23% Sample Variance 432641530431.364 New SD: 685.3123780843 p(x=18478) 0.06% Kurtosis 10.9998853724 p(x<16978

## Without

 Price Mean 18478 Standard Error 433.4296046906 Median 18550 Mode ERROR:#N/A Standard Deviation 1370.6247561686 Sample Variance 1878612.22222222 Kurtosis -1.3456954168 Skewness -0.4165890254 Range 3725 Minimum 16270 Maximum 19995 Sum 184780 Count 10 Confidence Level(95.0%) 980.4858848196

## Sheet1

 Vehicle type year make model price mpg (city) mpg (hwy) seating suv 2021 Honda Pilot 40,900 20 27 7 suv 2017 Buick Encore 15,500 25 33 5 suv 2020 Ford Escape 27,290 23 31 5 suv 2017 Nissan Pathfinder 20,998 20 27 7 suv 2018 Ford Explorer 27,755 19 27 7 suv 2018 Dodge Journey 15,469 17 25 7 suv 2019 Volkswagen Tiguan 28,000 22 28 7 suv 2020 Chevrolet Tahoe 62,706 14 23 8 suv 2018 Chevrolet Equinox 18,504 26 32 5 suv 2019 Toyota Highlander 25,200 21 27 5 Mean: 28,232 Median: 26,245 SD: 14,264 Sample size: 10 New SD 7132.2027406218 Mean-500 27732 0.4720552043 Mean+1000 29232 0.4442473547 Mean 28232 0.5 mean+/- 1500 26732