document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=626694>Question 626694</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I could use some help getting my thoughts and formulas together. Could you help me with this problem please.\r<BR>\n" );
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document.write( "The diameters of apples in a certain orchard are normally distributed with a mean of 4.45 inches and a standard deviation of 0.42 inches. Show all work. <BR>\n" );
document.write( "(A) What percentage of the apples in this orchard is larger than 4.38 inches? <BR>\n" );
document.write( "(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.38 inches?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #394390 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=394390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diameters of apples in a certain orchard are normally distributed with a mean of 4.45 inches and a standard deviation of 0.42 inches. Show all work. <BR>\n" );
document.write( "(A) What percentage of the apples in this orchard is larger than 4.38 inches?<BR>\n" );
document.write( "z(4.38) = (4.38-4.45)/0.42 = -0.17<BR>\n" );
document.write( "P(x > 4.38) = P(z > -0.17) = normalcdf(-0.17,100) = 0.5662 = 56.62%<BR>\n" );
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document.write( "(B) A random sample of 100 apples is gathered and the mean diameter is calculated. What is the probability that the sample mean is greater than 4.38 inches?<BR>\n" );
document.write( "z(4.38) = (4.38-4.45)/[0.42/sqrt(100)) = -1.67<BR>\n" );
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document.write( "P(x-bar > 4.38) = P(z > -1.67) = normalcdf(-1.67,100) = 0.9525 = 95.25%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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