MATH302 WEEK 4 DISCUSSION

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American Military University *

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302

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Statistics

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Jan 9, 2024

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docx

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Uploaded by carelessvicki

1. 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. Using my data with the type of cars I calculated with a mean of 68026.5 and a SD of 1157661.1. Assume that the 4 additional cars are randomly sampled, and their prices are recorded. What is the Probability that the sample mean price of the 4 new cars will be less than $500. The probability is already in the less than form, P( ? < 500), so ̅ I do not need to do additional work in Excel to find the probability. I also notice that the new sample size is n = 4. The mean will stay the same, but I will need to calculate a new SD. I will apply the Central Limit Theorem to do this. Remember you need to put in the “=” sign and then I will click on the cell that contains the old SD, and will hit the “ / “ sign and then use the SQRT( ) function and put 4 within the parentheses because the new sample size is 4. My new SD is 578830.5498 Next, we want to find this probability P( ? < 500) and we will ̅ use the NORM.DIST() function in Excel to do this. P( ? < 500) = NORM.DIST(500, 68026.5, 578830.55 , true) ̅ The probability that the sample mean for the new sample of 4 cars is below $500 is 45.36%. 2. 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.

Because of the words “higher than”, we want to find this probability P( ? > 1,000). Since we are using the same data the ̅ mean and the new SD will be the same. Remember the function in Excel are in the less than form. This means we will need to do an extra step in Excel to get the probability we want. P( ? > 1,000) = 1 - NORM.DIST(500,68026.5,578830.55,TRUE) ̅ The probability that the sample mean for the new sample of 4 cars is below $1,000 is 55.64%. 3. 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. Because of the word “exact”, we want to find this probability P( ? = 68026.5) Since we are using the same data the mean and ̅ the new SD will be the same. Remember the function in Excel are in the less than form. This means we will need to do an extra step in Excel to get the probability we want. =NORM.DIST(E14,E14,F27,TRUE)- NORM.DIST(E14,E14,F27,TRUE) The probability that the sample mean for the new sample of 4 cars is is equal to the mean is 0%. 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. Because of the word “between”, we want to find this probability P(Mean-1500 < ? < Mean +1500). Since we are using the same ̅ data the mean and the new SD will be the same. Remember the function in Excel are in the less than form. This means we will need to do an extra step in Excel to get the probability we want.

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