Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $510

And we can find the probability using the normal standard distribution table and with the complement rule we got:

Step-by-step explanation:

For this problem we have the following parameters:

We select a sample size of n =100 and we want to find this probability:

The distribution for the sample mean using the central limit theorem would be given by:

And we can solve this problem with the z score formula given by:

And if we find the z score formula we got:

And we can find the probability using the normal standard distribution table and with the complement rule we got: