Histogram of averages of iid random variables:

averages=Table[ Mean[ RandomVariate[HypergeometricDistribution[8,20,50],80] ], 10000];
h=Histogram[averages,{2,5,0.1},"PDF"]

mean = Mean[HypergeometricDistribution[8,20,50]]

sd=StandardDeviation[HypergeometricDistribution[8,20,50]]

Show[h,Plot[PDF[NormalDistribution[mean, sd/Sqrt[80]],x],{x,2,5},PlotRange->All]]

Probability calculation for the problem about tomatoes:

Probability[380<T<410,T\[Distributed]NormalDistribution[400,3Sqrt[40]]]//N