document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189874>Question 189874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please assist me with the following question.  I am having problems with distribution of z scores.  The distribution process is very confusing for me.  I greatly appreciate someone helping me with this problem and showing the steps for completion.  The problem is:\r<BR>\n" );
document.write( "\n" );
document.write( "The test scores for 2000 students were normally distributed with a mean of 65 and a standard deviation of 5.  Find the following:\r<BR>\n" );
document.write( "\n" );
document.write( "a. The z-score corresponding to the test score of 70.<BR>\n" );
document.write( "b. The probability that a tested student will have a score between 65 and 70. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142495 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=142495\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The problem is: <BR>\n" );
document.write( "The test scores for 2000 students were normally distributed with a mean of 65 and a standard deviation of 5. <BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Help yourself by illustrating each problem you have.<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "Draw a normal curve on an x-axis.  Mark the mean = 65 in the middle<BR>\n" );
document.write( "Note that s = 5<BR>\n" );
document.write( "----------------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Find the following: <BR>\n" );
document.write( "a. The z-score corresponding to the test score of 70.<BR>\n" );
document.write( "Use the formula z(x) = (x-u)/s<BR>\n" );
document.write( "z(70) = (70-65)/5 = 5/5 = 1<BR>\n" );
document.write( "Note: That means the score of 70 is one standard deviation to the right<BR>\n" );
document.write( "of the mean.<BR>\n" );
document.write( "----------------------\r<BR>\n" );
document.write( "\n" );
document.write( "b. The probability that a tested student will have a score between 65 and 70.<BR>\n" );
document.write( "Draw a normal curve over a z-axis.<BR>\n" );
document.write( "The z-score of 70 is 1 (above).<BR>\n" );
document.write( "The z-score of 65 is 0 because 65 is the mean.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "P(65 < x < 70) = P(0 < z < 1) = 0.34<BR>\n" );
document.write( "You have to use a calculator or a z-chart to find that probability.<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" );