Question 395259
I presume that by distribution being mound-shaped that implies that its normally distributed.
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a) If the production line is operating correctly, approximately what proportion of batches from a days' production will contain less than 1.84% of zinc phosphid?
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let x=% of zinc phosphid
Assuming Normally distribution with mean=2.0 and standard deviation=0.08
P(x<1.84)=P(z<(1.84-2)/.08)=P(z<-2.0)=0.02275 or 2.3% of batches
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b) Suppose one batch chosen randomly actually contains 1.80% zinc phosphide. Does this indicate that there is too little zinc phosphide in today's production? Explain your reasoning.
P(x<1.80)=p(z<-2.5)=0.00621 or 0.62%  This is highly unlikely from a normal distribution centered at 2.0 and std dev=0.08.  This implies that the sample was obtained from a distribution centered lower than 2.0