Newbie with a question
Greetings from the Heartland! I'm a doc student with enough math savvy to put on the head of a pin. STATS is required and passing it, mandatory. My question right now is probably a simple one, but it's driving me nuts. The question on my homework is this:
Reply With QuoteGreetings! I'll attempt an answer:
Yes, I think you have to assume the data is normally distributed. Because we'll be needing to calculate areas under the normal distribution probability curve, we'd better change everything to Z scores so we can use the standard tables.
Remember that to change a raw score into a Z score, we first subtract the mean from the raw score and then divide by the SD.
The z score of 75 is then 1.25, that of 43 is -2.75 and that of 73 is 1. This means that the raw score 75 is 1.25 standard deviations above the mean, 43 is 2.75 standard deviations below the mean etc.
Now we have to calculate areas under the standard normal curve (standard in that the mean is 0 and the SD is 1). I assume you have a method for doing this using tables or a calculator or something similar.
First you want to know what percentage of scores is above 75. To do this, you can first find the cdf (cumulative distribution function) value of the standard normal distribution at the z score for 75 (i.e. at 1.25). Using my calculator this is .8944. This is the area under the curve from minus infinity to 1.25, which is great if the question asked for the proportion of scores below 75. To get the answer just subtract it from 1, since the proportion of scores below 75 plus the proportion above 75 must equal 1. Hence the proportion is 0.1056, or as a percentage, 10.56%.
For the second question, let's write the area under the normal curve from minus infinity to your desired point x as cdf(x). What you want is the area under the curve between two points a and b. This is simply cdf(b) - cdf(a). Try calculating the answer with the z scores given above. I got 0.8383 as the answer, and expressed as a percentage 83.83%. How did you go?
