What is the probability that Upper X less than 95 or Upper X greater than 105? The probability that Upper X less than 95 or Upper X greater than 105 is nothing. (Round to four decimal places as needed.)

And for the other case if we use the z score and the complement rule we have:

And we can find the probability of interest like this:

And replacing 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 variable of interest of a population, and for this case we know the distribution for X is given by:

We assume that the distribution is  

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 find the individual probabilities we got:

And for the other case if we use the z score and the complement rule we have:

And we can find the probability of interest like this:

And replacing we got:

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted