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Hunter Chemical Company: Quantitative Analysis

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Hunter Chemical Company claims that its major product contains on the average 4.0 fluid ounces of caustic materials per gallon. It further states that the distribution of caustic materials per gallon is normal and has a standard deviation of 1.3 fluid ounces.

a. What proportion of the individual gallon containers for this product will contain more than 5.0 fluid ounces of caustic materials?

b. A government inspector randomly selects 100 gallon-size containers of the product and finds the mean weight of caustic material to be 4.5 fluid ounces per gallon. What is the probability of finding the mean of a sample of 100 that is 4.5 or greater? Do you think the production process was producing its usual level of caustic materials when this sample was taken?

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This solution uses step by step calculations and explanations to determine proportion and probability in order to solve the problems.

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Hunter Chemical Company claims that its major product contains on the average 4.0 fluid ounces of caustic materials per gallon. It further states that the distribution of caustic materials per gallon is normal and has a standard deviation of 1.3 fluid ounces.

a. What proportion of the individual gallon containers for this product will contain more than 5.0 fluid ounces of caustic materials?

Solution. Let X be the amount of fluid ounces of caustic materials per gallon that Hunter Chemical Company's major product contains. Then X ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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