The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104

And we can use the complement rule and the normal standard distribution or excel and 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 IQ of a population, and for this case we know the distribution for X is given by:

Where and

We select a sample of n = 50 and we want to find the probability that:

Since the distribution for X is normal then we know that the distribution for the sample mean is given by:

And we can use the z score formula given by:

And using this formula we got:

And we can use the complement rule and the normal standard distribution or excel and we got: