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Answer:
First part
And for this case we can use the z score formula given by:
And using this formula we got:
And we can use the normal standard table or excel and we got:
Second part
For the other part of the question we want to find the following probability:
And using the score we got:
And we can find this probability with this difference:
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 data of a population, and for this case we know the distribution for X is given by:
Where and
First part
And for this case we want this probability:
And for this case we can use the z score formula given by:
And using this formula we got:
And we can use the normal standard table or excel and we got:
Second part
For the other part of the question we want to find the following probability:
And using the score we got:
And we can find this probability with this difference: