The volume of liquid delivered by a high-precision agricultural drone, V V\,V litres, is normally distributed such that V∼N(12.5,0.62)V \sim \text{N}(12.5, 0.6^2)V∼N(12.5,0.62).
Five drones are selected at random to spray a field.
Calculate the probability that their combined volume is greater than 64.0 litres.
The concentration of a specific reagent in pharmaceutical vials, C C\,C mg/L, is distributed such that C∼N(45.0,1.22)C \sim \text{N}(45.0, 1.2^2)C∼N(45.0,1.22).
Two vials are selected at random from the production line.
Calculate the probability that the magnitude of the difference in their reagent concentrations exceeds 1.5 mg/L.
The mass of a specialized shipping frame, H H\,H kg, follows the distribution H∼N(20.0,0.5)H \sim \text{N}(20.0, 0.5)H∼N(20.0,0.5).
The random variable T T\,T represents the total weight of a fully assembled unit comprising one frame, whose mass is independent of HHH, packed with 12 electronic components, where each component has a mass K∼N(5.2,0.152)K \sim \text{N}(5.2, 0.15^2)K∼N(5.2,0.152) kg.
Given that T T\,T and H H\,H are independent,
Calculate P(T<0.8H+68.0)P(T < 0.8H + 68.0)P(T<0.8H+68.0)