document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=730917>Question 730917</A>: <I><SPAN STYLE=\"word-break: break-all;\"> New York receives an average of 35.4 inches of rain each year with a standard deviation of 4.2 inches. Assume a normal model applies.<BR>\n" );
document.write( "What is the probability that a student (in this area) will see an AVERAGE of less than 30 inches of rain in their four years?\r<BR>\n" );
document.write( "\n" );
document.write( "I know the probability of getting less than 30 in one year is 9.85%. I am just unsure about the average for the combination of the 4 years.\r<BR>\n" );
document.write( "\n" );
document.write( "z(30) = (30 - 35.4) / 4.2 = 1.286 (z-score) -> 0.0985<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #446921 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=446921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> New York receives an average of 35.4 inches of rain each year with a standard deviation of 4.2 inches. Assume a normal model applies.<BR>\n" );
document.write( "What is the probability that a student (in this area) will see an AVERAGE of less than 30 inches of rain in their four years? <BR>\n" );
document.write( "I know the probability of getting less than 30 in one year is 9.85%. I am just unsure about the average for the combination of the 4 years. <BR>\n" );
document.write( "z(30) = (30 - 35.4) / 4.2 = 1.286 (z-score) -> 0.0985<BR>\n" );
document.write( "-------<BR>\n" );
document.write( "In 4 years you have a sample of size n = 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The Central Limit Theorem says the standard deviation then 4.2/sqrt(4) = 2.1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(30) = (30-35.4)/2.1 = -2.5714<BR>\n" );
document.write( "P(x-bar < 30) = P(z < -2.5741) = normalcdf(-100,-2.5741) = 0.005 or 0.5%<BR>\n" );
document.write( "==========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "========================== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );