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Answer:
And using the normal standard distribution or excel we got:
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 weights of a population, and for this case we know the distribution for X is given by:
Where and
Since the dsitribution for x is normal then we know that the distribution for the sample mean is given by:
We want to find this probability:
And we can use the z score formula given by;
And if we find the z score for the limits given we got:
So we can calculate this probability like this:
And using the normal standard distribution or excel we got: