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standard deviation

Forums › Ask ACCA Tutor Forums › Ask the Tutor ACCA MA – FIA FMA › standard deviation

  • This topic has 1 reply, 2 voices, and was last updated 1 year ago by John Moffat.
Viewing 2 posts - 1 through 2 (of 2 total)
  • Author
    Posts
  • August 22, 2022 at 12:04 am #663879
    kashafaltaf500
    Participant
    • Topics: 29
    • Replies: 10
    • ☆

    The weights of a certain mass-produced item are known, over a long
    period of time, to be normally distributed with a mean of 8 kg and a
    standard deviation of 0.02 kg.
    Required:
    (a) If items whose weight lies outside the range 7.985 – 8.035 kg are
    deemed to be faulty, what percentage of products will be faulty?
    (b) If it is required to reduce the percentage of items that are too
    heavy (with weight over 8.035 kg) to 2%, to what value must the
    mean weight be decreased, leaving all other factors unchanged?
    (c) If it is required to reduce the percentage of items that are too light
    (with weight below 7.985 kg) to 2%, to what value must the
    standard deviation be decreased, leaving other factors
    unchanged?

    hi sir can u please explain how to solve B and C i don’t understand it at all i have watched your lecture videos too plz help

    August 22, 2022 at 11:22 am #663919
    John Moffat
    Keymaster
    • Topics: 56
    • Replies: 53174
    • ☆☆☆☆☆

    For (b), if 2% are above 8.035kg then 48% (or 0.48) will be between the mean and 8.035 kg.

    Working backwards in the tables. the ‘z’ value that gives an answer of 0.48 is 2.05 standard deviations.

    Therefore the distance between the mean and 8.035 must be 2.05 x 0.02kg = 0.041kg

    Therefore the mean will have to be 8.035 – 0.041 = 7.994 kg.

    (c) uses the same logic 🙂

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