The length of time it takes customers of a payday lender to repay their loan has a mean of 18 days and a standard deviation of 5 days . For a random sample of 40 borrowers , what is the probability that their mean payback time will be: i.) under 17 days ii.) over 20 days iii.) Between 17 and 20 days
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 length of time it takes customers of a payday lender to repay their loan has a
i.) under 17 days
ii.) over 20 days
iii.) Between 17 and 20 days
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