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sweet [91]
2 years ago
5

Bags of pretzels are sampled to ensure proper weight. The overall average for the samples is 9 ounces. Each sample contains 25 b

ags. The standard deviation is estimated to be 3 ounces. The upper control chart limit (for 99.7% confidence) for the average would be ________ ounces.
Mathematics
1 answer:
77julia77 [94]2 years ago
4 0

Answer:

The value is UCL  =  10.8  

Step-by-step explanation:

From the question we are told that

    The sample mean is  \= x  =  9 \  ounce

    The sample size is  n =  25

    The standard deviation is  \sigma =  3 \ ounce

Given that the sample size is not large enough i.e  n<  30  we will make use of the student t distribution table  

From the question we are told the confidence level is  99.7% , hence the level of significance is    

      \alpha = (100 -99.7 ) \%

=>   \alpha = 0.003

Generally the degree of freedom is  df =  n- 1

=>  df =  25 - 1

=>  df =  24  

Generally from the student t distribution table the critical value  of  \frac{\alpha }{2} at a degree of freedom of df =  24   is  

   t_{\frac{\alpha }{2} , 24 } = 3.0

Generally the margin of error is mathematically represented as  

      E = t_{\frac{\alpha }{2} , 24} *  \frac{\sigma }{\sqrt{n} }

=>     E = 3.0 *  \frac{3 }{\sqrt{25} }

=>     E =1.8

Gnerally the  upper control chart limit  for 99.7% confidence is mathematically represented as

         UCL  =  \= x  + E

=>      UCL  =  9 + 1.8  

=>      UCL  =  10.8  

     

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