The population mean annual salary for plumbers is $46,700.  A random sample of 42 plumbers is drawn from this population.  What is the probability (to three significant figures) that the mean salary of the sample is less than $44,000?  Assume «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#963;«/mi»«mo»=«/mo»«/math»$5600.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mover»«mi»x«/mi»«mo»§#175;«/mo»«/mover»«mo»§lt;«/mo»«mo»$«/mo»«mn»44«/mn»«mo»,«/mo»«mn»000«/mn»«/mrow»«/mfenced»«mo»=«/mo»«/math» {#1}