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.

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- August 22, 2022 at 12:04 am #663879
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 #663919For (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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