Television sets are hired out by a rental company. The time X in months between major repairs has an exponential distribution with mean 20 months. i. Find, to 3 significant figures, the probability that a television set hired out by the company will not require a major repair for at least two year period. ii. Find the median of X. iii. The company agrees to replace any set for which the time betwee
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!
Television sets are hired out by a rental company. The time X in months between major
repairs has an exponential distribution with mean 20 months.
i. Find, to 3 significant figures, the probability that a television set hired out by the
company will not require a major repair for at least two year period.
ii. Find the median of X.
iii. The company agrees to replace any set for which the time between major repairs
is less than M months. However, the company does not want to replace more than
one set in five such sets. Find the integer value that should be fixed for M.
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