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I am revising for my assignment on Normal Distribution but I do not understand my lecture note.

An IQ test is applied to a population of adults. The scores, X, on the test are found to be normally distributed with. Adults scoring more than 140 on the test are classified as ‘genius’. The mean is 100 and standard deviation is 15.

X~N(100,15^2)

The probability that an adult chosen at random achieves a ‘genius’ classification is 0.00383. I dont understand how we get to that answer. Please can someone explain this to me?

Thank you very much

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First find the z score of the desired score of 140. In this case, 140 is 2.66... standard deviations above the mean (or 15 * 2.66... = 40). Looking this up on a z table or using a calculator with this function, we can establish that 0.99617 of the scores are below this score and therefore 0.00383 are above it (given all the probabilities add to 1). I think the problem you are encounting is that within you're normal distribution function you've written N(100, 15^2) without any real reason to do 15^2. This will be likely what is causing you grief.

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  • $\begingroup$ Sorry Im a bit slow, when you say using a calculator. I use Classwiz Casio 991Ex, do you mind talking me thru what I need to pop in the calculator please? Is it Normal PD? $\endgroup$ – PeddiePooh Apr 12 '20 at 23:31
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    $\begingroup$ If you go into MODE -> STATISTICS and select 1 (for single variable data).You can then press AC to remove the grid and then OPTN to bring up a series of options. By scrolling down one page and selecting 4 (Norm Dist) a series of functions will show up. Here there are 3 functions: P, Q and R. These functions all take in the z score and P gives the percentage of scores below the given z score, Q gives the percentage of scores between the mean and the given z score, and R gives the percentage of scores above the given z score. So if you input R(2.66...) it should give you the desired result. $\endgroup$ – ajax2112 Apr 12 '20 at 23:44

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