The compressive strength of samples of cement can be modeled by a normal distribution with a mean of 6,098 kilograms per square centimeter and a standard deviation of 103 kilograms per square centimeter. Determine the probability a sample's strength is exactly 6,076 kilograms per centimeter squared. Round your answer to two decimal places.

By definition since in a continuous probability distribution the area below a line is 0

If the real question is:

We can use the z score formula given by:

If we apply this formula to our probability we got this:

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

And if the question is we apply the complement rule and 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 strengths of a population, and for this case we know the distribution for X is given by:

Where and

For this case we want

And by definition since in a continuous probability distribution the area below a line is 0

If the real question is:

We can use the z score formula given by:

If we apply this formula to our probability we got this:

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

And if the question is we apply the complement rule and we got:

(3x-8) or (3x+8)

step-by-step explanation: