So, that'll give us that orange and then we'll subtract that from one. Proportion is less than 2.5 standard deviations above the mean. So now, we can look at a z table to figure out what So, the z score here, z score here is a positive 2.5. So, he is 2.5 standardĭeviations above the mean. But how many standard deviations is that? Well, each standard deviation is three, so what's 7.5 divided by three? This just means the previousĪnswer divided by three. We know what that's gonna be, that's 7.5. We would take 47.5 and we would subtract the mean. Under the curve is one, so if we can figure out this orange area and take one minus that, And then, we can take one minus that to figure out the They give us the proportion that is below a certain z score. Proportion is below that because that's what z tables give us.
How many standard deviationsĪbove the mean is that? Then, we will look at a z table to figure out what So, the way we will tackle this is we will figure out Normal distribution curve that is above 47.5. Proportion of exam scores are higher than Ludwig's score? So, what we need to do is figure out what is the area under the Standard deviation is three points, so this could be one standardĭeviation above the mean, that would be one standardĭeviation below the mean. The mean is 40 points, so that would be 40 Look something like that, trying to make that What proportion of exam scores are higher than Ludwig's score? Give your answer correct Ludwig got a score ofĤ7.5 points on the exam. With a mean of 40 points and a standard deviation of three points. A set of philosophy exam scores are normally distributed if you have more intuitive or definitive solution, please enlighten me.īy the way, thanks for your clear explanation as always Sal and your answer might be related to the fact that the area of a line must be 0. I guess this might be so clear and easy to someone who is so familiar with the concept of probability. even though the probability of a student would get as high as 47.5 like Ludwig's is surely low (around 0.62% as we checked above), it is almost certain that the probability of the event of a student missing 1 problem thus getting 47.5 score is higher than 0 by the design of the test. thus any students missing 1 problem would get 47.5 points as their score. Let us picture or imagine this, the test has 50 as full score and 1 problem has 2.5 points.
Then must there be 0% of students having 47.5 as their score? The z-table says 99.38% of students would get less than 47.5 score and the answer for the problem given says 0.62% of them would get higher than 47.5. Something is bothering me on the probability of getting the exact same score of Ludwig (47.5 in this case) by other students.
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