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Math Help - Normal distribution problem

  1. #1
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    Post Normal distribution problem

    The Grounds Coffee Company has an automatic coffee packing machine that processes 2 million hundred grams packets of coffee annually. Past experience reveals that this machine fills packets of weights that follow a normal distribution with a standard deviation of 2 grams. To avoid prosecution for underweight packets, the management of the company prepared the following policy.
    Policy A: Fill the packets in such a way that the probability of packets having coffee less than hundred grams shall never exceed 0.0013.The machine has been set according to Policy A.
    A sales promotion team of Accuracy Machine Incorporation approaches the management of the coffee company for the purchase of a new machine supplied by their company. The team guarantees that as per report of research and development department of the company,the new machine has the same capacity of work as the present machine and has better accuracy since the weights of 100 grams filled by their machine follow normal distribution with standard deviation of only 1 gram.
    The cost of machine is Rs.400000.Since the present machine is in good condition the management of the coffee company decides that it will replace it's present machine only if the new machine is expected to pay for itself in one year without breaking the Policy A.
    Now, should the company purchase the new machine? Give reasons in support of your answer. Cost of 100 grams coffee is Rs.20.
    Note: Use your own country's currency if you so wish.
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  2. #2
    Grand Panjandrum
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    Re: Normal distribution problem

    Quote Originally Posted by Vinod View Post
    The Grounds Coffee Company has an automatic coffee packing machine that processes 2 million hundred grams packets of coffee annually. Past experience reveals that this machine fills packets of weights that follow a normal distribution with a standard deviation of 2 grams. To avoid prosecution for underweight packets, the management of the company prepared the following policy.
    Policy A: Fill the packets in such a way that the probability of packets having coffee less than hundred grams shall never exceed 0.0013.The machine has been set according to Policy A.
    A sales promotion team of Accuracy Machine Incorporation approaches the management of the coffee company for the purchase of a new machine supplied by their company. The team guarantees that as per report of research and development department of the company,the new machine has the same capacity of work as the present machine and has better accuracy since the weights of 100 grams filled by their machine follow normal distribution with standard deviation of only 1 gram.
    The cost of machine is Rs.400000.Since the present machine is in good condition the management of the coffee company decides that it will replace it's present machine only if the new machine is expected to pay for itself in one year without breaking the Policy A.
    Now, should the company purchase the new machine? Give reasons in support of your answer. Cost of 100 grams coffee is Rs.20.
    Note: Use your own country's currency if you so wish.
    Well, what is the mean weight of packet fill with each machine to meet the specified probability limit for being underweight?

    So how much will the new machine save per year?

    CB
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  3. #3
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    Re: Normal distribution problem

    Mean weight of packet fill would be 106 grams for the present machine and 103 grams for the new machine if both machines has been set as per policy A.
    The number of packages having coffee in excess of 100 grams would be 19,97,400 and number of packages having less than 100 grams of coffee would be 2,600. Rs.1.2 is cost of 6 grams of coffee. Rs.0.6. is cost of 3 grams of coffee.
    So,Company would incur losses of about Rs.23,93,760 if the company used present machine.
    And company would incur losses of about Rs.11,96,880 if the company used new machine.
    Hence there would be savings of Rs.7,96,880 (deducting cost of machine from total savings of Rs.11,96,880)
    I would advise the company to purchase the machine.
    What is your opinion? Am i right?
    Answer is not available in the paper set.
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