Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3.what is p?
a) 0.469b) 0.956c) 0.493d) 0.490e) 0.466f) none of the above

If we assume that the deviation is then the solution is:

f) None of the above

If we assume that the deviation is then the solution is:

b) 0.956

Step-by-step explanation:

1) 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".  

2) Solution to the problem

Let X the random variable that represent the variable 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 on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

If we assume that the deviation is then the solution is:

And we can find this probability on this way:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

#7 is correct it is the first option