A random sample of n = 9 structural elements is tested for comprehensive strength. We know the true mean comprehensive strength μ = 5500 psi and the standard deviation is σ = 100 psi. Find the probability that the sample mean comprehensive strength exceeds 4985 psi. (Express your result to four significant digits.)

And the z score is given by:

And using this formula we got:

And using the complement rule and the normal tandard distribution or excel 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 comprehensive strength of a population, and for this case we know the following info:

Where and

We select a sample size of n=9. Assuming that the distribution for X is normal then we can use the distribution for the sample mean is given by:

And we want this probability:

And the z score is given by:

And using this formula we got:

And using the complement rule and the normal tandard distribution or excel we got:

x^6

step-by-step explanation:

this is correct because:

x-6=0

0*x=0

so

x^6