For a randomly chosen adult staying in Condominium Merak, X represents the time, in minutes, spent per week exercising in the gym of the condominium. Y represents the time, in minutes, spent per week jogging in the open area. Xis modelled by Normal Distribution with mean 65 and variance 13, whereas Y is modelled by Normal Distribution with mean 32 and variance 5. Assuming that the time spent in gym is independent with the time spent in jogging. The total time spent working out per week for a randomly chosen adult staying in Condominium Merak is denoted by X+1.5Y. An adult staying in Condominium Merak is chosen at random. Find the probability that this adult spends more than 2 hours working out per week. Find the probability that this adult spends at least 30 minutes more on exercising in the gym of the condominium than jogging in the open area.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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