Indicated probability or percentage of sampling error

I have tried this problem for three days, and I cannot find the example of how to do this in my book, or online anywhere.

Scores on an apptitude test are normally distributed with a mean of 220 and a standard deviation of 30. What is the probability that the sampling error made in estimating the population mean by the mean of a random sample of 50 test scores will be at most 5 points?

I know that the answer is .762, but I don't know how to get there. I hope someone can show me.



TS Contributor
You want to find the probability of getting a sample mean somewhere between 215 and 225.

z1 = (215-220)/4.2426
z2 = (225-220)/4.2426

If you look at my post called "The Vaunted Normal Distribution" under the examples section, you'll see how to compute the probability between z1 and z2.