document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=619302>Question 619302</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can anyone help me with this? I need to show my work but not sure what steps I need to take to solve this.\r<BR>\n" );
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document.write( "X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:<BR>\n" );
document.write( "(A) P(x < 77.0)<BR>\n" );
document.write( "(B) P(75.0 < x < 85.0)<BR>\n" );
document.write( "(C) P(x > 85.0) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389587 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=389587\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> X has a normal distribution with a mean of 80.0 and a standard deviation of 3.5. Find the following probabilities:<BR>\n" );
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document.write( "The measuring stick you have to use to find probabilities <BR>\n" );
document.write( "is the z-chart or technology that you have available.<BR>\n" );
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document.write( "(A) P(x < 77.0)<BR>\n" );
document.write( "z(77) = (77-80)/3.5 = -3/3.5 = -0.8571<BR>\n" );
document.write( "That simply means 77 is 0.8571 standard deviations below the mean.<BR>\n" );
document.write( "Now use your z-chart to find the probability to the left of -0.8571<BR>\n" );
document.write( "Ans: normalcdf(-100,-0.8571) = 0.1957<BR>\n" );
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document.write( "(B) P(75.0 < x < 85.0)<BR>\n" );
document.write( "z(75) = (75-80)/3.5 = -1.4286<BR>\n" );
document.write( "z(85) = (85-80)/3.5 = +1.4286<BR>\n" );
document.write( "P(75<x<85) = P(-1.4286 < z < +1.4286) = normalcdf(-1.4286,+1.4286) = 0.8469<BR>\n" );
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document.write( "(C) P(x > 85.0)= P(z > 1.4286) = normalcdf(1.4286,100) = 0.0766<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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