So far I was able to calculate the mean and standard deviation, where Mean = 23

Question

So far I was able to calculate the mean and standard deviation, where Mean = 23 and standard deviation = 6.6 or 6.7 if we round.

In the solution the professor first subtracted the mean from the standard deviation and had an answer of 16.3, and then he set up a table and had the the z-score formula next to it. Let's say he calculated the Z-score for each grade, then how do I know how many people failed based on that?

I really don't understand whats going on in the problem, can someone PLEASE give me a detailed explanation on that? I'm desperate for help!!!

A class consists of 11 students who recently took a test. The results are shown below (out of 60 points): 20, 15, 26, 32, 18, 28, 35, 14, 26, 22, 17 Most students didn't even get 30 out of 60, and most will fail. The professor decides to standardize all the grades and only fail people 1 standard deviation below the mean. Determine the failing grades.

Explanation / Answer

if you just want to calculate number of fails then you don't need to calculate z value

simply failing threshold = 23-6.7 = 16.3

so less than it will fail i.e 15,14 will fail.

for calculating probability of failing students assuming normal

z = (x- mean)/sigma = 1(given)

and calculate cumulative prob. under 1

note: z= 1 also gives us

x = mean +sigma ; which i have used to calculate above.

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