SOLUTION: Hello!
My question is :
A machine fills containers with a mean weight per container of 16 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, the standard de
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-> SOLUTION: Hello!
My question is :
A machine fills containers with a mean weight per container of 16 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, the standard de
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Question 1030308: Hello!
My question is :
A machine fills containers with a mean weight per container of 16 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, the standard deviation of the weights equal? (assume normality)
With these types of problems, I have been really confused on the process on how to get to the answer. Any help would be greatly appreciated!!
You can put this solution on YOUR website!
Question:
Hello!
My question is :
A machine fills containers with a mean weight per container of 16 oz. If no more than 5% of the containers are to weigh less than 15.8 oz, the standard deviation of the weights equal? (assume normality)
With these types of problems, I have been really confused on the process on how to get to the answer. Any help would be greatly appreciated!!
Solution:
Given
mean (μ)=16 oz.
left-tail=5% at 15.8 oz.
Also, from the probability distribution (using a calculator or tables), 5% corresponds to -1.644854 in a standard normal distribution (μ=0, σ=1), as shown below:
We can now convert this value back to the real-world problem using the relationship:
Z=(X-μ)/σ
transposing,
σ=(X-μ)/Z = (15.8-16)/(-1.644854) = 0.1215914
Answer: the required standard deviation is 0.1216 (to 4 decimals)
