Final answer:
The 50% increase in crop yield for a newly engineered strain does not affect the variance of the crop yields. Variance is a measure of dispersion and remains the same if the change is strictly a proportional increase in the average yield, with the spread of data unchanged.
Step-by-step explanation:
When we talk about crop yields and their modeling, we are discussing a concept in Mathematics, closely related to the statistics and probability domain. If a newly engineered crop strain presents a 50% increased yield, this is referring to a scale change in the mean of the yield distribution but doesn't automatically impact the variance. The variance of a normal random variable is a measure of dispersion that indicates how much the values of the variable are spread out.
For a normal distribution, if you increase the mean yield by 50%, the variability or spread of the data does not inherently change. Therefore, assuming other factors remain constant and there is just an increase in mean yield due to improved characteristics such as increased resistance of crops to environmental stresses or increased nutritional qualities of food crops, the variance remains the same. Variance would only change if the variability of yield from plant to plant was affected, which is not implied by an across-the-board increase in yield.