7. The following table represents the new members that have been acquired by a fitness center. New members 45 60 57 Month Jan Feb March April 65 Assuming a = 0.3, ß = 0.4, an initial forecast of 40 for January, and an initial trend adjustment of 0 for January, use exponential smoothing with trend adjustment to come up with a forecast for May on new members.
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!
Given, = 0.3 and = 0.4. The initial forecast is equal to 40.
The trend adjusted exponential smoothing is computed as
and the exponentially smoothed and exponentially smoothed trend parts are computed as follows:
where is the smoothing constant,
is the trend smoothing constant,
F1 is the initial forecast, T1 is the initial trend forecast
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