Afilling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces. forty jars filled by this machine are selected at random. what is the probability that the mean amount per jar filled in the sampled jars is less than 3.9 ounces

A filling machine puts an average of four ounces of coffee in jars, with a standard deviation of 0.25 ounces fourty jars filled by this machine are selected at random.

The probability that the mean amount per jar filled in the sampled jars is less than 3.9 ounces will be 0.006. is 4oz. using Z-score concept.We will solve this problem with the help of the z-score concept.

Z-score concept is a Numerical measurement which describes the value's relationship to the mean group of values . Z-score is always measure in terms of standard deviation from the mean.  

If Z-score = 0, it shows that the datas point score is identical to the mean.

The sample of standard deviation here is

Thus, The Z-score here represents ,

Here, we must find the area under the standard normal curve which lies to the left of  

We will use a table of Z-scores concept or calculator which built-in statistics functions.

According to TI-83 Plus calculator, that area will be 0.006.  

Therefore, Here we interprete standard deviation, the volume of coffee put into the jars are very close to the mean 4 oz.

Learn more about Z-score here :link

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