Respuesta :
Let's attack this problem using the z-score concept. The sample std. dev. here is (0.25 oz)/sqrt(40), or 0.040. Thus, the z score representing 3.9 oz. is
3.9 - 4.0
z = -------------- = -2.5
0.040
In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5. Use a table of z-scores or a calculator with built-in statistics functions. According to my TI-83 Plus calculator, that area is
0.006. One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.
3.9 - 4.0
z = -------------- = -2.5
0.040
In one way or another we must find the area under the std. normal curve that lies to the left of z = -2.5. Use a table of z-scores or a calculator with built-in statistics functions. According to my TI-83 Plus calculator, that area is
0.006. One way of interpreting this that with so small a standard deviation, most volumes of coffee put into the jars are very close to the mean, 4 oz.
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.
What is Z-scope 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
[tex]\rm \dfrac{0.25 oz}{\sqrt{40} } or\; 0.040[/tex]
Thus, The Z-score here represents ,
[tex]\rm=3.9 oz =\dfrac{3.9-4.0}{0.040}\\\\z=-2.5[/tex]
Here, we must find the area under the standard normal curve which lies to the left of [tex]z=-2.5[/tex]
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 :https://brainly.com/question/13299273
