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Amount of zinc phosphide in commercial rat poison. A
Chapter , Problem 166SE(choose chapter or problem)
Amount of zinc phosphide in commercial rat poison. A chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat populations in sugarcane fields. 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 rat 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 a standard deviation of .08%.
a. If the production line is operating correctly, approximately what proportion of batches from a day’s production will contain less than 1.84% of zinc phosphide?
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.
Questions & Answers
QUESTION:
Amount of zinc phosphide in commercial rat poison. A chemical company produces a substance composed of 98% cracked corn particles and 2% zinc phosphide for use in controlling rat populations in sugarcane fields. 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 rat 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 a standard deviation of .08%.
a. If the production line is operating correctly, approximately what proportion of batches from a day’s production will contain less than 1.84% of zinc phosphide?
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:Solution :
Step 1 of 2:
The given information explain about amount of zinc phosphide in commercial rat poison.
Our goal is:
a). We need to find what proportion of batches from a day’s production will contain less
than 1.84% of zinc phosphide.
b). We need to find does this indicate that there is too little zinc phosphide in today’s
production and explain our reasoning.
a).
If the production line is operating correctly, approximately then we have to find what proportion of batches from a day’s production will contain less than 1.84% of zinc phosphide.
From the given information we know that the distribution is mound-shaped.
Now we can use the Empirical Rule.
Here 1.84% is 2 standard deviation below the mean.
Then the Empirical Rule states that approximately 95% of the observation will fall within 2 standard deviation of the mean and approximately 5% will lie outside that interval.
We know that mound-shaped distribution is symmetric.
Then approximately 2.5% of the days production of batches will fall below 1.84% .