Reference no: EM132836596
The normal distribution I and II
Start by reviewing the following Handy Helper, which is also provided in this week's Lesson: Week 4 Normal Probabilities.pdf. This document will give you step by step examples on how to use Excel to calculate probabilities using the Central Limit Theorem and the Normal Distribution. DO NOT do these calculations by hand. Let Excel do the heavy lifting for you.
Next, use your vehicle data identified in Week 1 ( see excel file), and find the mean and standard deviation for your car prices. Once you find your mean and standard deviation, assume those are the population mean, μ, and population standard deviation, σ. Next assume that car prices are normally distributed. Solve the following:
1. If you were to find another random sample of 4 different car prices, what is the probability that the sample mean of the new 4 cars will be less than $500 below the mean of your original data? Interpret your results.
o HINT: we need to calculate the standard error when the sample size is 4. Additionally, we need to find the value that is $500 below the mean of your original data. For example, if your original mean for the 10 cars you observed in week 1 was $15,000, then $500 below the mean would be $14,500. Thus, the probability you want to find is P(X¯ < 14,500)
2. If you were to find another random sample of 4 different car prices, what is the probability that the sample mean of the new 4 cars will be higher than $1,000 above the mean of your original data? Interpret your results.
o HINT: Use the same logic as above. If the mean of your original data 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).
3. If you were to find another random sample of 4 different car prices, what is the probability that the sample mean of the new 4 cars will be within $1,500 of the mean of your original data? Interpret your results.
o HINT: Use the same logic as above. If the mean of your original data is $15,000, then $1,500 within your mean is 15,000 - 1,500 = $13,500 and 15,000 + 1,500 = $16,500. Thus the probability you would want to find is P(13,500 < X¯ < 16,500).
4. If you were to randomly sample 1 additional car, what is the probability that the new car price will be at least $43,000? Thus, find the following probability: P(X ≥ 43,000)
5. compare the probabilities that you found, were they higher/lower and why?
Instructions: Your initial post should be at least 150 words. Also, you MUST attach your Excel file with the formulas that you used to solve the questions above. 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.
Attachment:- Normal Probabilities - With and WO CLT.rar