# A confusing (for me) stats/probability problem

I'm having a problem with this question:

Record shows that the students in a certain university has mean IQ of 115 with a standard deviation of 10. A research conducted on 30 students showed a mean IQ of 110. What is the probability that the sample of 30 students will have a mean IQ less than 115?

Our class came up with 3 different answers:

A.) .9969
They computed this using 110 as the population mean. [(115-110) / (10/√30)] then z-table.

B.) .0031
They computed this using 115 as the population mean then 110 as the random variable. [(110-115) / (10/√30)] then z-table.

C.) .5000
They computed this using 115 as the population mean then 115 as the random variable. [(115-115) / (10/√30)] then z-table.

• The question you were asked is not as clear as it might be, as it depends on what "the sample of 30 students" refers to. If it refers to the sample already taken, the probability is 100%, since that sample actually had a mean IQ of $110 < 115$. If it's a whole new sample, it's C, as the population from which the new sample is drawn has a mean of 115, so that's the appropriate population mean to use. In this latter case, the 110 has nothing to do with it, because it refers to the old sample, which is different to the new one, so it's not clear why it's here except to confuse. Feb 17, 2018 at 16:38