IQ scores and normal distributions


I would like to hear your opinions on the normality of scores on an IQ test. The test had 30 questions and apart from the general IQ score separate subtest scores such as mathematics, verbal and spatial IQ were also calculated.

Here is a list of results that were obtained from the data.

I would like to report standardized scores and percentiles for the general score and all subtest scores. However I was told that all scores and subtest scores had to follow a normal distribution before this could happen.

Thanks for all your help


Note: The skewness and kurtosis results seem to be in the required range. I then read that they should be divided by the standard error, but when this happens the results became way too large. Similarly the Shapiro-Wilk statistic is close to 1 but the significance is 0. How does this affect the normality result?