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Thread: Worded problem

  1. #1
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    Worded problem

    Hi I am stuck on this this question, could someone please help me.

    Thnx maties
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  2. #2
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    Re: Worded problem

    Each trial is her shooting at goal, and in each trial there are only two possibilities, shooting a goal or missing. So p = 0.7 and n is unknown.

    We want to evaluate n such that $\displaystyle \begin{align*} \textrm{Pr}\,\left( X \geq 50 \right) = 0.99 \end{align*}$, so

    $\displaystyle \begin{align*} 1 - \textrm{Pr}\,\left( X < 50 \right) &= 0.99 \\ 1 - \sum_{k = 0}^{49}{ {n\choose{k}} \left( \frac{7}{10} \right) ^k \left( \frac{3}{10} \right) ^{n - k} } &= \frac{99}{100} \end{align*}$

    You will need to solve this with a CAS.
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  3. #3
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    Re: Worded problem

    let $G$ be a random variable that counts how many goals Monique makes.

    $G$ has a binomial distribution with parameters $n$, and $p=0.7$

    We need to determine $n$ such that $P[G \geq 50] \geq 0.99$

    I'm not sure what tools you have to work with to try and solve for $n$, there is no simple closed formula for it.

    Can you give me some idea of what your professor expects?

    Are you supposed to use software?

    Are you supposed to make an approximation?
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  4. #4
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    Re: Worded problem

    Quote Originally Posted by romsek View Post
    let $G$ be a random variable that counts how many goals Monique makes.

    $G$ has a binomial distribution with parameters $n$, and $p=0.7$

    We need to determine $n$ such that $P[G \geq 50] \geq 0.99$

    I'm not sure what tools you have to work with to try and solve for $n$, there is no simple closed formula for it.

    Can you give me some idea of what your professor expects?

    Are you supposed to use software?

    Are you supposed to make an approximation?
    There IS a closed formula for it, see my previous post. Unfortunately there is not a way to solve it through algebraic means. The OP will be expected to solve it with a CAS calculator.
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  5. #5
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    Re: Worded problem

    Quote Originally Posted by Prove It View Post
    There IS a closed formula for it, see my previous post. Unfortunately there is not a way to solve it through algebraic means. The OP will be expected to solve it with a CAS calculator.
    I call that a closed form equation.

    It's not a closed form formula.

    But this is picky. One way or the other it will have to be solved with software. (or a lot of patience)
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