The variable M denotes the cost of the main course, in dollars, and the variable D the cost of the dessert. The variable T denotes the total cost of a two-course meal: T= M+ D. (i) Find the mean and variance of M. (ii) Find the mean and variance of D. (iii) List all the possible two-course meals, giving the price for each one.

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1 The menu at a café is shown below.
Main coursе
Dessert
Fish and Chips
$3
Ice Cream
$1
Apple Pie
Sponge Pudding
Spaghetti
$3.50
$1.50
Pizza
$4
$2
Steak and Chips $5.50
The owner of the café says that all the main-course dishes sell equally well, as
do all the desserts, and that customers' choice of dessert is not influenced by
the main course they have just eaten.
Transcribed Image Text:1 The menu at a café is shown below. Main coursе Dessert Fish and Chips $3 Ice Cream $1 Apple Pie Sponge Pudding Spaghetti $3.50 $1.50 Pizza $4 $2 Steak and Chips $5.50 The owner of the café says that all the main-course dishes sell equally well, as do all the desserts, and that customers' choice of dessert is not influenced by the main course they have just eaten.
The variable M denotes the cost of the main course, in dollars, and the variable
D the cost of the dessert. The variable T denotes the total cost of a two-course
meal: T= M+ D.
(i) Find the mean and variance of M.
(ii) Find the mean and variance of D.
(iii) List all the possible two-course meals, giving the price for each one.
(iv) Use your answer to part (iii) to find the mean and variance of T.
(v) Hence verify that for these figures
mean (T) = mean (M) + mean (D)
%3D
and
variance (T) = variance (M) + variance (D).
Transcribed Image Text:The variable M denotes the cost of the main course, in dollars, and the variable D the cost of the dessert. The variable T denotes the total cost of a two-course meal: T= M+ D. (i) Find the mean and variance of M. (ii) Find the mean and variance of D. (iii) List all the possible two-course meals, giving the price for each one. (iv) Use your answer to part (iii) to find the mean and variance of T. (v) Hence verify that for these figures mean (T) = mean (M) + mean (D) %3D and variance (T) = variance (M) + variance (D).
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