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A machine dispenses water into a glass. assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces, the average amount of water dispensed by the machine is

Respuesta :

LammettHash
[tex]f_X(x)=\begin{cases}\frac1{16-10}=\frac16&\text{for }10\le x\le16\\0&\text{otherwise}\end{cases}[/tex]

[tex]\implies\mathbb E(X)=\displaystyle\int_{-\infty}^\infty xf_X(x)\,\mathrm dx=\int_{10}^{16}\frac x6\,\mathrm dx=13[/tex]

Answer:

⇢ [tex]{\boxed{\bold{Average \: amount = 13 \: ounces}}}[/tex]

Step-by-step-explanation:

Given question:-

⇢ A machine dispenses water into a glass. Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces.

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Find:-

⇢ The average amount of water dispensed by the machine is

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Calculations:-

⇢ Let us assume 'a and b' as the first ounce and the second ounce.

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  • [tex]\rm{a = 10 \: ounce}[/tex]
  • [tex]\rm{b = 16 \: ounce}[/tex]

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⇢ [tex]{\boxed{\bold{\dfrac{(a + b)}{2}}}}[/tex]

⇢ [tex]\rm{\dfrac{(10 + 16)}{2}}[/tex]

⇢ [tex]\rm{\cancel{\dfrac{26}{2}}}[/tex]

⇢ [tex]{\boxed{\bold{13 \: ounces}}}[/tex]

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Therefore, 13 ounces is the average amount of water dispensed by the machine.

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