Answer:
The chain of supermarkets must order 428.1 gallons of milk.
Step-by-step explanation:
Let's define the random variable X.
X : ''Weekly volume of sales in thousands of gallons''
X is a continuous random variable.
The probability density function for X is
[tex]f(x)=7(1-x)^{6}[/tex] when 0 < x < 1
[tex]f(x)=0[/tex] Otherwise.
Let's denote as ''a'' to the quantity of milk for the question.
We are looking for :
[tex]P(X>a)=0.02[/tex]
[tex]P(X>a)=\int\limits^1_a {f(x)} \, dx[/tex]
[tex]P(X>a)=\int\limits^1_a {7(1-x)^{6}} \, dx[/tex]
[tex]P(X>a)=(1-a)^{7}[/tex]
[tex](1-a)^{7}=0.02[/tex]
[tex]a=1-\sqrt[7]{0.02}[/tex]
[tex]a=0.4281[/tex]
a is in thousands of gallons, therefore the chain of supermarkets must order
428.1 gallons of milk in order to satisfy the question.
