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Answer:
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".
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 following conditions
Where and
And for this case we select a sample size of n= 15. and we want to know the distribution for the sample mean . We can assume that the distribution for
is approximately normal and given by:
Asuming that the distribution for X is also approximately normal. So then the parameters are: