document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257493>Question 257493</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have a final today and there will be similar questions as this one. Can someone please help me understand this problem.\r<BR>\n" );
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document.write( "The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? (b) More than 590 MPa? (c) Less than 600 MPa?<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189418 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=189418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The fracture strength of a certain type of manufactured glass is normally distributed with a mean of 579 MPa with a standard deviation of 14 MPa. (a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? (b) More than 590 MPa? (c) Less than 600 MPa?<BR>\n" );
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document.write( "You have to convert to z-scores.<BR>\n" );
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document.write( "(a) What is the probability that a randomly chosen sample of glass will break at less than 579 MPa? <BR>\n" );
document.write( "z(579)= (579-579)/14 = 0<BR>\n" );
document.write( "P(x < 579) = P(z < 0) = 0.5000<BR>\n" );
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document.write( "(b) More than 590 MPa? <BR>\n" );
document.write( "z(590) = (590-579)/14 = 11/14= 0.7857...<BR>\n" );
document.write( "P(x > 590) = P(z > 0.7857..) = 0.2160...<BR>\n" );
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document.write( "(c) Less than 600 MPa?<BR>\n" );
document.write( "z(600) = (600-579)/14 = 21/14 = 3/2<BR>\n" );
document.write( "P(x < 600) = P(z< 3/2) = 0.9332<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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