1. The number of girls who attend a summer basketball camp has been recorded for
ID: 2901198 • Letter: 1
Question
1. The number of girls who attend a summer basketball camp has been recorded for the seven years the camp has been offered. Use exponential smoothing with a smoothing constant of .8 to forecast attendance for the eighth year.
47, 68, 65, 92, 98, 121, 146
2. A trend line for the attendance at a restaurant's Sunday brunch is given by
Number = 264 + .72(t)
How many guests would you expect in week 20?
3. Super Cola sales breakdown as 90% regular soda and 10% diet soda. While 60% of the regular soda is purchased by men, only 30% of the diet soda is purchased by men. If a woman purchases Super Cola, what is the probability that it is a diet soda?
4. A mail order company tracks the number of returns it receives each day. Information for the last 40 days shows
Number of days
5. To establish a driver education school, organizers must decide how many cars, instructors, and students to have. Costs are estimated as follows. Annual fixed costs to operate the school are $50,000. The annual cost per car is $5000. The cost per instructor is $13,000 and one instructor is needed for each car. Tuition for each student is $300. Let x be the number of cars and y be the number of students.
Number of returnsNumber of days
0-99 10 100-199 15 200-299 9 300 or more 6Explanation / Answer
1) The initial forecast has been taken as the average of the first 3 months and then the calculations have been done on the basis of that
The formula is Forecast for t+1 = (smoothing constant*attendance) + (1 - smoothing constant)*(Forecast of t)
2) Trendline Number = 264 + .72(t)
Put t = 20 (Assuming the t is weekly data) else (if t is daily then put t = 141 and t = 147 and subtract)
For t =20 we have number = 264+ .72(20) = 278.4
3)
Regular soda purchased by men = 60% = 0.6 * 0.9 = 0.54 Super Cola
Diet soda purchased by men = 30% = 0.3 * 0.1 = 0.03 Super Cola
0.57 Super Cola is purchased by men
Hence 1-0.57 = 0.43 Super Cola is purchased by women
Prob it is diet soda =(1 - 0.3) * 0.43 = 0.7*0.43 = 0.301 = 30.1%
4)
1. All sample point probabilities must lie between 0 and 1 (i.e. 0 pi 1).
2. The probabilities of all the sample points within a sample space P must sum to 1
5)
Month Attendance Forecast Forecast for t+1 1 47 60 50 2 68 50 64 3 65 64 65 4 92 65 87 5 98 87 96 6 121 96 116 7 146 116 140 8 140Related Questions
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