plz

Dishwasher powder is poured into the cartons by an automatic dispensing machine which is set to dispense 3 kg of powder into each carton. In order to check that the dispensing machine is working to an acceptable standard, a production engineer takes a random sample of 60 cartons and weighs them. It is found that the mean weight of the sample is 3.005 kg. It is known that the dispensing machine operates with a variance of 576 g2 [Hint: take note of the measurement units!] Perform an appropriate Z-test to evaluate whether the dispensing machine is operating to the designed specications. The manufacturer of the dishwasher powder is willing to rely on a 1% level of signicance