Answer to Question #153440 in Statistics and Probability for Shavetra

Question

1. Attendance at Orlando’s newest Disneylike attraction, Lego World, has been as follow:

QUARTER

GUEST (IN THOUSADS)

QUARTER

GUEST (IN THOUSADS)

Winter Year 1

73

Summer Year 2

124

Spring Year 1

104

Fall Year 2

52

Summer Year 1

168

Winter Year 3

89

Fall Year 1

74

Spring Year 3

146

Winter Year 2

65

Summer Year 3

205

Spring Year 2

82

Fall Year 3

98

a) Compute the Seasonal Indices using all the data.

b) If the expected guest for the next year (i.e., Forth Year) is 550000, forecast the quarterly attendance for the year 4?

Answer 1

a)

$$Guests\ (Demand) \\$$

$$\begin{matrix} Quarter & Year1& Year2 & Year3 \\ Winter & 73 & 65 & 89 \\ Spring & 104 & 82 & 146 \\ Summer & 168 & 124 & 205\\ Fall & 74 & 52 & 98 \end{matrix}$$

$$Average\ Demand=\dfrac{73+65+89}{3}=\dfrac{227}{3}=75.67$$

$$Average\ Demand=\dfrac{104+82+146}{3}=\dfrac{332}{3}=110.67$$

$$Average\ Demand=\dfrac{168+124+205}{3}=\dfrac{497}{3}=165.67$$

$$Average\ Demand=\dfrac{74+52+98}{3}=\dfrac{224}{3}=74.67$$

$$Total \ Average \ annual\ demand$$

$$=\dfrac{227+332+497+224}{3}=\dfrac{1280}{3}=426.67$$

$$Total \ Average \ quaterly\ demand$$

$$\dfrac{1280}{3(4)}=\dfrac{320}{3}=106.67$$

$$Seasonal \ index =\dfrac{\dfrac{227}{3}}{\dfrac{320}{3}}=\dfrac{227}{320}=0.709375$$

$$Seasonal \ index =\dfrac{\dfrac{332}{3}}{\dfrac{320}{3}}=\dfrac{332}{320}=1.037500$$

$$Seasonal \ index =\dfrac{\dfrac{497}{3}}{\dfrac{320}{3}}=\dfrac{497}{320}=1.553125$$

$$Seasonal \ index =\dfrac{\dfrac{224}{3}}{\dfrac{320}{3}}=\dfrac{224}{320}=0.700000$$

$$\begin{matrix} Quarter & Seasonal \ index\\ Winter & 0.709375 \\ Spring & 1.037500 \\ Summer & 1.553125 \\ Fall & 0.700000 \end{matrix}$$

b)

$$Winter=\dfrac{550}{4}\times 0.709375=97.539 (thousands)$$

$$Spring=\dfrac{550}{4}\times 1.037500=142.656(thousands)$$

$$Summer=\dfrac{550}{4}\times 1.553125=213.555 (thousands)$$

$$Fall=\dfrac{550}{4}\times 0.700000=96.250 (thousands)$$

$$\begin{matrix} Quarter & Seasonal \ index & Guest (thousands)\\ Winter & 0.709375 & 97.539 \\ Spring & 1.037500 & 142.656 \\ Summer & 1.553125 & 213.555\\ Fall & 0.700000 & 96.250 \end{matrix}$$