using raw scores for standard deviation

Hi,

I am rubbish at maths, so I apologise for if this question is very simple...

I am trying to calculate whether a child is eligible for exam dispensation. To be eligible, it states that they must have 'an average, standardised score of 84 or less'.

I have tested speed of writing. A study of 2701 people found that the average writing speed for a child of his age is 17.8 words per minute (wpm). He wrote at a speed of 11.3wpm.

If I assume that there will be a normal distribution of the scores, is there a way of working out whether or not the child meets the criteria for exam dispensation (i.e. his standardised score is less than 84?)

Thanks
Frantastic :)

Hey frantastic.

When you say 84 is that a percentile? (In other words, is the score in the lower 84% of scores for the normal distribution)?

If this is the case calculate the test statistic z = (11.3 - 17.8)/sd and find using either tables or a computer P(Z < z).

We can definitely say that it will be in the bottom 50% since 11.3 < 17.8 so it will definitely be in the bottom 84%.

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