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"The average mark in a grade 9 math class is 75.5% with a standard deviation of 9.5%. If Grade 9 math marks have a normal distribution:

b) Within what range of marks are 99.7% of all students?"

In a normal distribution curve, 99.7 percentile is a z-score of 2.75. How would I find the range of marks in this instance? Would I use the z-score formula?

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  • $\begingroup$ Yes, use the z-score formula. $\endgroup$
    – Kontorus
    Commented Jun 23, 2016 at 18:30
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    $\begingroup$ Also, 99.7 should be a z-score of 3. $\endgroup$
    – Kontorus
    Commented Jun 23, 2016 at 18:31
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    $\begingroup$ See stats.stackexchange.com/search?q=68-95-99.7 $\endgroup$
    – whuber ♦
    Commented Jun 23, 2016 at 18:39
  • $\begingroup$ consider adding the tag [self-study] $\endgroup$
    – Firebug
    Commented Jun 23, 2016 at 19:40

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http://www.oswego.edu/~srp/stats/6895997.htm

This may be of interest to you.

The range would be about (75.5 - 3*9.5, 75.5 + 3*9.5), but not exactly as normalcdf(-3,3) = 99.73. To get a bit more accurate you'd have to find the area of the end tips you don't want, (1-99.7)/2, and invNorm that. Would be like 2.999984, so 3 is probably good enough.

The z-score of 2.75 is referring to a graph starting at the far left up to 2.75 standard deviations, which is not what you want in this question.

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