document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=243016>Question 243016</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the<BR>\n" );
document.write( "human resource director shows the annual cost per employee per year followed the normal<BR>\n" );
document.write( "probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.<BR>\n" );
document.write( "a. What fraction of the employees cost more than $1,500 per year for dental expenses?<BR>\n" );
document.write( "b. What fraction of the employees cost between $1,500 and $2,000 per year?<BR>\n" );
document.write( "c. Estimate the percent that did not have any dental expense.<BR>\n" );
document.write( "d. What was the cost for the 10 percent of employees who incurred the highest dental<BR>\n" );
document.write( "expense? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #178061 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=178061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Shaver Manufacturing, Inc., offers dental insurance to its employees. A recent study by the human resource director shows the annual cost per employee per year followed the normal probability distribution, with a mean of $1,280 and a standard deviation of $420 per year.<BR>\n" );
document.write( "a. What fraction of the employees cost more than $1,500 per year for dental expenses?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a(1500) = (1500-1280)/420 = 220/420 = 0.5238<BR>\n" );
document.write( "P(x > 1500) = P(z > 0.5238) = 0.30 = 30%<BR>\n" );
document.write( "===============================================<BR>\n" );
document.write( "b. What fraction of the employees cost between $1,500 and $2,000 per year?<BR>\n" );
document.write( "z(2000) = (2000-1280)/420 = 1.7143...<BR>\n" );
document.write( "P(1500 < x < 2000) = P(0.5238 < z < 1.7143) = 0.257<BR>\n" );
document.write( "-----------------------------------------------<BR>\n" );
document.write( "c. Estimate the percent that did not have any dental expense.<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(0) = (0-1500)/420 = -3.5714..<BR>\n" );
document.write( "P(x < 0) = P(z < -3.4714) = 0.0002589..<BR>\n" );
document.write( "==========================================<BR>\n" );
document.write( "d. What was the cost for the 10 percent of employees who incurred the highest dental expense?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "invNorm(0.90) = z = 1.2816<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = zs+u<BR>\n" );
document.write( "x = 1.2816*420+1280<BR>\n" );
document.write( "x = $1818.25<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" );