Hypothesis test problem

When you say the variation is 13cm, do you mean the max to min, the standard deviation or the variance? Are you assuming all distributions are normal? What you need to know is the variance or standard deviation. If the standard deviation is 13cm and you sample 41 products, the expected standard deviation in the mean of those sampled would be 13/sqrt(41) = 2.03. The z value for 95% confidence is 1.96, so the deviation on the mean 3.98 so yes, 116 would be different than 120 since that is a difference of 4.00

You need to learn the difference between the words "height" and "weight." Weight is not measured in centimeters, so native speakers of English should be able to figure out what you mean. However, not everyone is a native speaker of English, and you would just unnecessarily confuse people by speaking about "weight" in terms of "cm."