SOLUTION: A chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat population in sugarcane field. Production must be ca

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Question 395259: A chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat population in sugarcane field. Production must be carefully controlled to maintain the 2% zinc phosphide because too much zinc phosphide will cause damage to the sugarcane and too little will be ineffective in controlling the rate population. Records from past production indicate that the distribution of the actual percentage of zinc phosphide present in the substance is approximately mound-shaped with a mean of 2.0% and standard deviation o 0.08%.
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?
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.
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
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