A manufacturer of biscuits produces a large variety of different flavours and types. One particular type, the Cream Shor

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A manufacturer of biscuits produces a large variety of different
flavours and types. One particular type, the Cream Shorty’s are
produced to be 9cm long. If they are too long they don’t fit in the
packaging in which they are sold and need to be discarded. To
monitor the process the manufacturer randomly selects 12 biscuits
every 10 minutes and measure the average length of the biscuits in
the sample. If the average length falls in either the top or the
bottom 5% of lengths they need to adjust the process.
If the biscuits are supposed to be manufactured according to a
normal distribution with a mean of 9cm and a standard deviation of
0.2cm what is the upper and lower limit within which the sample
mean must lie in order for the process to be allowed to
continue?