Answer:
And using the normal standard table or excel we can find this probability with this difference:
Step-by-step explanation:
For this case we define the random variable X="metal shafts" produced in a manufacturing company, and we have the following properties given:
Previous concepts
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
They select a sample if size n=4, by the central limit theorem the distribution for the sample mean is given by:
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we use this formula we got this:
And using the normal standard table or excel we can find this probability with this difference: