# The normal distribution i and ii

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. 