The number of miles that a particular car can run before its battery wears out is exponentially distributed with an average of 5,000 miles. Hence, the probability that the lifetime of the battery is greater than 5000 miles is 0.368. The car has already completed a 10000-mile trip without any battery failure, what is the probability that the car will be able to complete another 5000-mile trip without having to replace the car battery? a). 0.368 b). 0.135 c). 0.632 d).1
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!
The number of miles that a particular car can run before its battery wears out is exponentially distributed with an average of 5,000 miles. Hence, the probability that the lifetime of the battery is greater than 5000 miles is 0.368. The car has already completed a 10000-mile trip without any battery failure, what is the probability that the car will be able to complete another 5000-mile trip without having to replace the car battery?
a). 0.368 b). 0.135 c). 0.632 d).1
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