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 $500

And we can find this probability using the normal standard distribution and we got:

Step-by-step explanation:

For this case we have the foolowing parameters given:

represent the mean

represent the standard deviation

the sample size selected

And for this case since the sample size is large enough (n>30) we can apply the central limit theorem and the distribution for the sample mean would be given by:

And we want to find this probability:

We can use the z score formula given by:

And we can find this probability using the normal standard distribution and we got:

y=mx+