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Math Help - 20% of memory chips.....

  1. #1
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    20% of memory chips.....

    Question :

    20% of memory chips made in certain plant are defective. Find the probability that in a lot of 100 randomly chosen for inspection.
    i) atmost 15 will be defective
    ii) exactly 15 will be defective
    Obtain these probability also by using Normal Approximation to binomial probabilities.
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    Quote Originally Posted by zorro View Post
    Question :

    20% of memory chips made in certain plant are defective. Find the probability that in a lot of 100 randomly chosen for inspection.
    i) atmost 15 will be defective
    ii) exactly 15 will be defective
    Obtain these probability also by using Normal Approximation to binomial probabilities.
    If X is the random variable 'number of defective chips', what is n? What is p? What do you know about the normal approximation to the binomial distribution?

    Please show what you know and state exactly where you are stuck.
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    I am stuck here

    Quote Originally Posted by mr fantastic View Post
    If X is the random variable 'number of defective chips', what is n? What is p? What do you know about the normal approximation to the binomial distribution?

    Please show what you know and state exactly where you are stuck.

    n = 100
    p = 0.20

    probability of getting exactly 15 defective is

    p(x, \lambda) = \frac{\lambda^x . e^{- \lambda}}{x!} = 0.05

    probability of getting atmost 15 defective is

    ?????

    And How to obtain the probability using normal approx to binomial prob
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    Quote Originally Posted by zorro View Post
    n = 100
    p = 0.20

    probability of getting exactly 15 defective is

    p(x, \lambda) = \frac{\lambda^x . e^{- \lambda}}{x!} = 0.05

    probability of getting atmost 15 defective is

    ?????

    And How to obtain the probability using normal approx to binomial prob Mr F says: Start by going to your class notes or textbook and reviewing that part of the course. You will also find on-line tutorials using Google.
    Why are you using the Poisson distribution? Is the Poisson approximation to the binomial distribution asked for? The fact is that X ~ Binomial(n = 100, p = 0.2) and you're probably expected to use technology to calculate the required probabilities.
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    Reason for using Poisson

    Quote Originally Posted by mr fantastic View Post
    Why are you using the Poisson distribution? Is the Poisson approximation to the binomial distribution asked for? The fact is that X ~ Binomial(n = 100, p = 0.2) and you're probably expected to use technology to calculate the required probabilities.

    The reason i was using poisson was because the sample size is large and i though when the sample size is too large poisson is used instead of Binomial dist..........
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    Quote Originally Posted by zorro View Post
    The reason i was using poisson was because the sample size is large and i though when the sample size is too large poisson is used instead of Binomial dist..........
    Since you're asked to find "Normal Approximation to binomial probabilities" I assumed that the binomial distribution was required ....

    Furthermore, are all the criteria for using the Poisson approximation to the binomial distribution satisfied for this situation?
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    Quote Originally Posted by mr fantastic View Post
    Since you're asked to find "Normal Approximation to binomial probabilities" I assumed that the binomial distribution was required ....

    Furthermore, are all the criteria for using the Poisson approximation to the binomial distribution satisfied for this situation?

    If u could please look at the question and please let me know because i am also not that good in this subject . I am still learning , would do as u say
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    Quote Originally Posted by zorro View Post
    If u could please look at the question and please let me know because i am also not that good in this subject . I am still learning , would do as u say
    Read all my replies again. They say what to do. Where exactly are you stuck?
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    I am stuck here

    Quote Originally Posted by mr fantastic View Post
    Read all my replies again. They say what to do. Where exactly are you stuck?

    I am actually now confused , on whether which distribution to use

    Binomial
    or
    Poisson
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    Quote Originally Posted by zorro View Post
    I am actually now confused , on whether which distribution to use

    Binomial
    or
    Poisson
    Binomial, as I have said or implied several times in this thread.
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    I am again stuck ?

    Quote Originally Posted by mr fantastic View Post
    Binomial, as I have said or implied several times in this thread.

    ii) exactly 15 are defective
    p(15,100,0.20) = \frac{100!}{15! . 95!} . (0.20)^{15} . (0.20)^{95} = 0.005

    i) at most 15 are defective ................Question 1
    how should i do this ...........

    P(x \le 15,100,0.20) = \sum_{x = 1}^{15} \frac{100!}{x! . (100 - x)!}  (0.20)^x . (1-0.20)^{100-x} ........Is this correct ...........

    Question 2)
    And fr Normal Approximation should i use the following formula below
    z = \frac{X - n \theta}{\sqrt{n \theta (1 - \theta)}}


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    Quote Originally Posted by zorro View Post
    ii) exactly 15 are defective
    p(15,100,0.20) = \frac{100!}{15! . {\color{blue}95}!} . (0.20)^{15} . ({\color{blue}0.20})^{{\color{blue}95}} = 0.005 Mr F says: Totally wrong. There are several basic mistakes (highlighted in blue).

    i) at most 15 are defective ................Question 1
    how should i do this ...........

    P(x \le 15,100,0.20) = \sum_{x = {\color{blue}1}}^{15} \frac{100!}{x! . (100 - x)!} (0.20)^x . (1-0.20)^{100-x} ........Is this correct ........... Mr F says: Not quite. The sum should start from x = 0.

    Question 2)
    And fr Normal Approximation should i use the following formula below
    z = \frac{X - n \theta}{\sqrt{n \theta (1 - \theta)}}

    Mr F says: Yes. But do to the calculation you will need to use the continuity correction.


    ..
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    About continutty correction

    Quote Originally Posted by mr fantastic View Post
    ..

    About continuity correction , i didnt get the part , hw should i exactly introduce it in my formula .Should i have to add 1 to the X or what ......or ?
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    Quote Originally Posted by zorro View Post
    About continuity correction , i didnt get the part , hw should i exactly introduce it in my formula .Should i have to add 1 to the X or what ......or ?
    Read this: The Binomial Distribution
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  15. #15
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    Is this correct

    Quote Originally Posted by mr fantastic View Post
    ..
    using continuity correction

    \therefore z = \frac{15.5 - n \theta}{\sqrt{n \theta \sqrt{1 - \theta}}}......Is this correct??

    If correct could u please provide me with an example on how such problems should be actually be solved ........for my future reference....
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