{(2, 3), (1, 5), (2, 7)} - NOT because 2->3 and 2->7 {(11, 9), (11, 5), (9, 3)} - NOT because 11->9 and 11->5 {(3, 8), (0, 8), (3, -2)}
- NOT because 3->8 and 3->-2
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for
Step-by-step explanation:
Previous concepts
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". The letter is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for