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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
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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