Answer:
49 cars
Step-by-step explanation:
Probability of cars to be sold in a week,a = 0.2
Probabiity of cars not sold in a week, b = 0.8
Number of cars estimated to be sold in a week = 20 and 60 cars in 3 weeks
Using, P(x) = nCx *(a)∧x * (b)∧n - x, where n = 3 weeks, x = 1 week
P(x=1) = 3C1 * (0.2) * (0.8)² = 3 X 0.2 X 0.64 X 60 cars = 23 cars
P(x=2) = 3C2 * (0.2)² * (0.8) = 3 X 0.04 X 0.8 X 60 cars =  6 cars
Number of cars three weeks from now: 20 + 23 + 6 = 49 cars
Answer:
The forecast of the number of cars 3 weeks from now is 52 cars.
Step-by-step explanation:
As per the trent the number of the cars per week is 5 cars
The current level of cars is 40 cars per week
Number of cars sold in current week=20 cars
Forecast of the cars sold 3 weeks from now is given as
[tex]L_t=\alpha Y_t+(1-\alpha)(L_{t-1}+T_{t-1})\\[/tex]
From the data
Y_t=20 cars
L_t-1=40 cars
T_t-1=5 cars
α=β=0.2
So the equation becomes
[tex]L_t=\alpha Y_t+(1-\alpha)(L_{t-1}+T_{t-1})\\L_t=0.2*20+(1-0.2)(40+5)\\L_t=40[/tex]
Now the trend is calculated as
[tex]T_t=\beta(L_{t}-L_{t-1})+(1-\beta)T_{t-1}[/tex]
By putting the values the equation becomes
[tex]T_t=\beta(L_{t}-L_{t-1})+(1-\beta)T_{t-1}\\T_t=0.2(40-40)+(1-0.2)5\\T_t=0+0.8*5\\T_t=4[/tex]
Now the forecast of the cars sale 3 weeks from now is given as
[tex]L_{t+k}=L_t+kT_t[/tex]
where k is 3 so
[tex]L_{t+k}=L_t+kT_t\\L_{t+3}=40+3*4\\L_{t+3}=40+12\\L_{t+3}=52\\[/tex]
So the forecast of the number of cars 3 weeks from now is 52 cars.
