Question: A certain system we have designed needs to be powered by a 24-V dc supply. Available to us in our lab are each of the following types of batteries whose statistical characteristics (and quantities available) are as shown in the table. The system can tolerate variations in the supply voltage that are within 1 V of the designed 24 V level. Anything outside that range will damage the system. Your job is to come up with a combination of the batteries that will lead to the highest probability that the combined supply voltage will remain within the range 23-25 V. Assume the voltage of each battery is a Gaussian random variable and is independent of the others and the means and standard deviations of each battery are as shown in the table. State how you would form some combination of the batteries available to produce the desired supply voltage. Also specify what is the probability that your combination of batteries falls within the desired range.
