Suppose tree diameters are normally distributed with mean 8.8 inches and standard deviation 2.8 inches. What is the probability that a randomly selected tree will be at least 10 inches in diameter?

And we can find this probability with this difference and using the normal standard table or excel:

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 diameters 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 normal standard table or excel: