statistics/probability

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QUESTION-
machines are used to pack sugar into packets supposedly
containing 1.20kg each.on testing a large number of packets over a
long perodof time ,it was found that the mean weight of the packets
was 1.24kg and the standard deviation was 0.04kg. a particular machine
is selected to check the total weight of each of the 25 packets filled
consecutively by the machine .calculate the limits within which the
weight of the packets should lie assuming that the machine is not been
classified as faulty.

  • statistics/probability -

     Mean weight of the packets = 1.24 kg
     Standard Deviation, SD = 0.04kg
     Variance = 0.04^2 = 0.0016
     Standard Error, SE = 0.04/sqrt (25) • = 0.04/5 = 0.008

     Considering 99.7% confidence level the means will lie between (1.2+3SE) and (1.2-3SE)
     Upper limit is 1.224kg
     Lower Limit is 1.176kg

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