1. The specification for the length of an engine is a minimum of 99mm and a maximum of 104.4mm. A batch of parts is produced that is normally distributed with a mean of 102mm and a standard deviation of 2mm. Parts cost GHs 10.00 to make, those that are too short have to be scrapped; those too long are shortened, at a further cost of GHs 8.00. a) Find the percentage of parts which are: i) undersize (ii) oversize; b) Find the expected cost of producing 1,000 usable parts; c) Calculate and explain the implication of changing the production method so that the mean is halfway between the upper and lower specification limits.

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1. The specification for the length of an engine is a minimum of 99mm and a maximum
of 104.4mm. A batch of parts is produced that is normally distributed with a mean of
102mm and a standard deviation of 2mm. Parts cost GHs 10.00 to make, those that are
too short have to be scrapped; those too long are shortened, at a further cost of GHs
8.00.
a) Find the percentage of parts which are: (i) undersize (i) oversize;
b) Find the expected cost of producing 1,000 usable parts;
c) Calculate and explain the implication of changing the production method so that the
mean is halfway between the upper and lower specification limits.
Transcribed Image Text:1. The specification for the length of an engine is a minimum of 99mm and a maximum of 104.4mm. A batch of parts is produced that is normally distributed with a mean of 102mm and a standard deviation of 2mm. Parts cost GHs 10.00 to make, those that are too short have to be scrapped; those too long are shortened, at a further cost of GHs 8.00. a) Find the percentage of parts which are: (i) undersize (i) oversize; b) Find the expected cost of producing 1,000 usable parts; c) Calculate and explain the implication of changing the production method so that the mean is halfway between the upper and lower specification limits.
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