A machine used to fill gallon-sized paint cans is regulated so that the amount o

Question

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 124 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 123.9 ounces. Does the machine need to be reset? Explain your reasoning A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 124 ounces and a standard deviation of 0.20 ounce. You randomly select 40 cans and carefully measure the contents. The sample mean of the cans is 123.9 ounces. Does the machine need to be reset? Explain your reasoning

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    123.9      
u = mean =    124      
n = sample size =    40      
s = standard deviation =    0.2      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -3.16227766      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -3.16227766   ) =    0.000782701

As this is a very small probability, then YES, THE MACHINE NEEDS TO BE RESET. [ANSWER]

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