Distributive property: distribute the to the by multiplying​

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Step-by-step explanation:

675656685177554742

Step-by-step explanation:

a)

And we can find this probability with this difference:

And using the norma standard distribution or excel we got:

b)

And using the complement rule 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".  

Part a

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

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 apply this formula to our probability we got this:

And we can find this probability with this difference:

And using the norma standard distribution or excel we got:

Part b

For this case we want this probability:

And we can use the z score and we got:

And using the complement rule we got: