Hi Peter:

Sorry for the delay in responding. We have been busy over the last couple of days.

The two statistics that are used as measure of normalcy are:
(i) "skewness" - is the data distributed evenly about the mean? A negative value indicates it peaks to the left of the mean and a postive value of the statistic indicates a lean to the right. A normal distribution has a skewness value of zero.
(ii) "kurtosis" (sounds like a contagious disease!) - how much weight is in the two tails, i.e. how fat are they. You could think of this as how strongly are the distribution values "attracted" to the mean, or, are there many values out at the two extremities? A normal distribution has a kurtosis value of 3. (Note that Excel's descriptive statistics is using what is called "excess kurtosis": i.e. kurtosis minus 3. Hence, the closer to zero the better the fit.)

There are various tests of how close a distribution is to being "normal", using these two statistics.

Your Column B distribution has a skewness of -0.105771427 and kurtosis of -1.191099665. Column C values are 0.018817645 and -0.224389706 (using Excel)

Go with Column E.

The big question, for me, is why does your client want these normally distributed numbers. What are they going to do with them?

Godfrey