document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1105424>Question 1105424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be the variable that represents the height of the individuals of a given population. Suppose that X has approximately normal distribution, with mean 170 cm and variance of 100 cm ^ 2.<BR>\n" );
document.write( "a) What is the probability that an individual of this population has height less than 175 cm?<BR>\n" );
document.write( "b) Find the points a and b, symmetric to the mean, such that P (a< x < b) = 0,50 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #720240 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=720240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Less than 175 is z<(175-170)/10, (x-mean)/sd, and sd is the sqrt (var)<BR>\n" );
document.write( "z<+(5/10) or +(1/2)<BR>\n" );
document.write( "Probability is 0.6915. <BR>\n" );
document.write( "The probability of being symmetric to the mean and having a probability of 0.50 requires the z-value of 0.2500 probability, which is +/-0.675<BR>\n" );
document.write( "z=0.675=(x-170)/10<BR>\n" );
document.write( "6.75=x-170<BR>\n" );
document.write( "x=176.75<BR>\n" );
document.write( "(163.25, 176.75) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );