Question

The weight specification for packets of noodles is 150±10 grams. The packet-filling process is in a state of statistical control and the packet weights are normally distributed with a standard deviation of 1.5 grams. However, the process is not centered at 150 grams.

a)Find the value for process mean so that only 4 packets in 1000 fall below the lower specification.

b)For the value of the process mean you found in part (i), what percent of the packets will be above the upper specification?

Answer 1

a)

µ =    145      
σ =    1.5      
          
P( X ≤    140   ) = P( (X-µ)/σ ≤ (140-145) /1.5)  
=P(Z ≤   -3.333   ) =   0.0004

Hence Mean = 145

b)

µ =    145                  
σ =    1.5                  
                      
P ( X ≥   160.00   ) = P( (X-µ)/σ ≥ (160-145) / 1.5)              
= P(Z ≥   10.000   ) = P( Z <   -10.000   ) =    0.0000   (answer)

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