Question 1118388
the population mean is 24215
the population standard deviation is 3678.


the sample size is 85.
the standard deviation of the distribution of sample means, called the standard error, from samples whose size is 85 is equal to 3678 / sqrt(85) = 398.9351119.


the z-score for a sample mean of 24500 or less from this population, with a sample size of 85, is z = (24500 - 24215) / 398.9351119 = .7143732313.


the area under the normal distribution curve to the left of this z-score is equal to  .7625107243.


that means the probability that you would get a sample of size 85 whose mean is 24500 or less is .7625107243, or approximately 76.25%.


this can be seen visually in the following graph.


<img src = "http://theo.x10hosting.com/2018/061003.jpg" alt="%%%" >