A customer in the wholesale garment trade is often entitled to a discount for a cash payment for goods. The amount of discount varies by vendor. A sample of 150 items selected from a population of 4,000 invoices at the end of a period of time revealed that in 13 cases, the customer failed to take the discount to which he or she was entitled. The amounts (in dollars) of the 13 discounts that were not taken were as follows: 6.45, 15.32, 97.36, 230.63, 104.18, 84.92, 132.76, 66.12, 26.55, 129.43, 88.32, 47.81, 89.01 Construct a 99% confidence interval estimate of the population total amount of discounts not taken
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!
A customer in the wholesale garment trade is often entitled to a discount for a cash payment for goods.
The amount of discount varies by vendor. A sample of 150 items selected from a population of 4,000
invoices at the end of a period of time revealed that in 13 cases, the customer failed to take the
discount to which he or she was entitled. The amounts (in dollars) of the 13 discounts that were not
taken were as follows:
6.45, 15.32, 97.36, 230.63, 104.18, 84.92, 132.76, 66.12, 26.55, 129.43, 88.32, 47.81, 89.01
Construct a 99% confidence
The 99% confidence interval can be determined using following formula:
The mean and standard deviation can be determined using (=average) and (=stdev.s) command:
Sample mean (x) = 86.066
Sample standard deviation (s) = 59.285
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