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Math Help - Find the maximum amount of cartons to be ordered...

  1. #1
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    Find the maximum amount of cartons to be ordered...

    Heres the question:

    A biscuit factory produces biscuits which are packed into its signature gift boxes. On average, 3% of these gift boxes are substandard.
    (i) Show that the probability that a randomly chosen batch of 30 gift boxes will contain at least 2 gift boxes which are substandard is 0.227, correct to 3 significant figures.

    The operations unit of the factory decided to pack 30 gift boxes into one carton before delivery to all its retail outlets.
    (ii) Find the probability that out of 10 randomly chosen cartons, there are more than 4 cartons with at least 2 substandard gift boxes.

    Every week, the owner of each retail outlet will place order with the factory.
    (iii) Find the maximum number of cartons to be ordered so that the chance of having no substandard gift box is more than 5%.


    I'm unsure how to solve the question in red.
    Could anybody help me with it? Thank you very much!!
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  2. #2
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    Re: Find the maximum amount of cartons to be ordered...

    Quote Originally Posted by pumbaa213 View Post
    Heres the question:

    A biscuit factory produces biscuits which are packed into its signature gift boxes. On average, 3% of these gift boxes are substandard.
    (i) Show that the probability that a randomly chosen batch of 30 gift boxes will contain at least 2 gift boxes which are substandard is 0.227, correct to 3 significant figures.

    The operations unit of the factory decided to pack 30 gift boxes into one carton before delivery to all its retail outlets.
    (ii) Find the probability that out of 10 randomly chosen cartons, there are more than 4 cartons with at least 2 substandard gift boxes.

    Every week, the owner of each retail outlet will place order with the factory.
    (iii) Find the maximum number of cartons to be ordered so that the chance of having no substandard gift box is more than 5%.


    I'm unsure how to solve the question in red.
    Could anybody help me with it? Thank you very much!!
    you have to go back to the original information, i.e. Pr[substandard box]=0.03

    Now find the probability that a carton of 30 has no substandard boxes.

    Pr[no substandard boxes in 30 box carton] = (1-0.03)^{30}=0.4

    Pr[no substandard boxes in N cartons] = (0.4)^N

    Solving this for 0.05 reveals N<3
    Thanks from pumbaa213
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  3. #3
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    Re: Find the maximum amount of cartons to be ordered...

    Thank you so much romsek!!!
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