A laboratory centrifuge operates at discrete vibration stages V V\,V where V∈{1,2,3,4,5,6,7,8}V \in \{1, 2, 3, 4, 5, 6, 7, 8\}V∈{1,2,3,4,5,6,7,8}, and each stage is equally likely to occur during a test cycle.
Determine the mean and the variance of VVV.
The centrifuge is monitored over 60 independent test cycles. By applying the Central Limit Theorem, calculate an estimate for the probability that the average vibration stage Vˉ\bar{V}Vˉ of these 60 cycles is less than 4.1.
