XYZ office supplies company leases copier machines to businesses. Leases are normally distributed with a mean of 24 months and variance of 36. a. What is the probability that a copier will still be on lease after 27 months? b. What is the probability that a copier will be returned within one year? c. What is the probability that a copier will be on lease for more than 15 months but will be returned before 30 months d. What is the probability that a copier will be on lease for a period less than 30. months e. What is the probability that a copier will be on lease for more than 6 months? f In the last financial year, the company leased 1000 machines. The rent received per machine is Rs 1000 per month. How many machines would have generated a rent of more than Rs 24000 g. What is the minimum lease period below which the bottom 10% lie? h. h.What is the minimum lease period of lease for the top 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!
XYZ office supplies company leases copier machines to businesses. Leases are
a. What is the probability that a copier will still be on lease after 27 months?
b. What is the probability that a copier will be returned within one year?
c. What is the probability that a copier will be on lease for more than 15 months but will be returned before 30 months
d. What is the probability that a copier will be on lease for a period less than 30.
months
e. What is the probability that a copier will be on lease for more than 6 months?
f In the last financial year, the company leased 1000 machines. The rent received per machine is Rs 1000 per month. How many machines would have generated a rent of more than Rs 24000
g. What is the minimum lease period below which the bottom 10% lie? h.
h.What is the minimum lease period of lease for the top 1% ?
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