document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=483103>Question 483103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.93 inches and a standard deviation of 0.59 inches.  Show all work. <BR>\n" );
document.write( "(A)  What percentage of the grapefruits in this orchard is larger than 5.88 inches? <BR>\n" );
document.write( "(B)  A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.88 inches? <BR>\n" );
document.write( "  Thanks much </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #330625 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=330625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diameters of grapefruits in a certain orchard are normally distributed with a mean of 5.93 inches and a standard deviation of 0.59 inches. Show all work. <BR>\n" );
document.write( "(A) What percentage of the grapefruits in this orchard is larger than 5.88 inches? <BR>\n" );
document.write( "----<BR>\n" );
document.write( "z(5.88) = (5.88-5.93)/0.59 = -0.0847<BR>\n" );
document.write( "P(x > 5.88) = P(z > -0.0847) = 0.5338<BR>\n" );
document.write( "=========================================== <BR>\n" );
document.write( "(B) A random sample of 100 grapefruits is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 5.88 inches?<BR>\n" );
document.write( "z(5.88) = (5.88-5.93)/[0.59/sqrt(100)] = -0.8475<BR>\n" );
document.write( "P(x-bar > 5.88) = P(z > -0.8475) = 0.8016<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" );