Question

Plastic sheeting produced by a machine must be periodically monitored for possible fluctuations in thickness. Uncontrollable variation in the viscosity of the liquid mold produces some variation in thickness. Based on experience with a great many samples, when the machine is working well, an observation on thickness has a normal distribution with standard deviation σ = 1.35 mm. Samples of 20 thickness measurements are collected regularly. A value of the sample standard deviation exceeding 1.4mm signals concern about the product. Find the probability that, when σ = 1.35, the next sample will signal concern about the product.

Answer 1

Sample Standard deviation = 1.35 / sqrt(20)

= 0.301869177

Now to have this standard deviation goes more than 1.4

= 1.4 / 0.301869177

= 4.637

Hence we have to get the probability to get value outside 4.637 S.D on either side of graph

µ =    0                  
σ =    1                  
                      
P ( X ≥   4.64   ) = P( (X-µ)/σ ≥ (4.63777061999956-0) / 1)              
= P(Z ≥   4.638   ) = P( Z <   -4.638   ) =    0.00000176

=0.00000176 * 2

= 0.000004

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