Answer to Question #265837 in Statistics and Probability for talie

Question

A child has been given a bottle of Appy apple drink of 350 millilitres and is asked to drink

and leave some for later, with quiet some resistance. Determine the following if the child drinks

uniform amounts.

(a) The probability that the child leaves less than 250 millilitres,

(b) The probability that the child drinks between 100 and 300 millilitres.

(c) The average amount left for later.

(d) The variance of the amount left for later.

Answer 1

a)

$$P(X<250)=\displaystyle\int_{0}^{250}\dfrac{1}{350}dx=[\dfrac{1}{350}x]\begin{matrix} 250 \\ 0 \end{matrix}$$

$$=\dfrac{5}{7}\approx0.7143$$

b)

$$P(100<X<200)=\displaystyle\int_{100}^{200}\dfrac{1}{350}dx=[\dfrac{1}{350}x]\begin{matrix} 200 \\ 100 \end{matrix}$$

$$=\dfrac{2}{7}\approx0.2857$$

c)

$$\mu_X=\dfrac{0+350}{2}=175$$

d)

$$Var(X)=\sigma_X^2=\dfrac{(350-0)^2}{12}\approx10208.33$$