document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198619>Question 1198619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 4 percent and a standard deviation of 1.0 percent. A single analyst is randomly selected. Find the probability that his/her forecast is\r<BR>\n" );
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document.write( "(a) At least 3.3 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( "(b) At most 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( "(c) Between 3.3 percent and 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<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 #832238 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=832238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 4<BR>\n" );
document.write( "standard deviation = 1\r<BR>\n" );
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document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.\r<BR>\n" );
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document.write( "in your problem:<BR>\n" );
document.write( "m = 4<BR>\n" );
document.write( "s = 1\r<BR>\n" );
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document.write( "when x = 3.3, the formula becomes:<BR>\n" );
document.write( "z = (3.3 - 4) / 1 = -.7<BR>\n" );
document.write( "area to the left of z = -.7 = .2419635782.<BR>\n" );
document.write( "area to the right of z = -.7 = 1 minus .2419635782 = .7580364128.\r<BR>\n" );
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document.write( "when x = 9, the formula becomes:<BR>\n" );
document.write( "z = (9 - 4) / 1 = 5<BR>\n" );
document.write( "area to the left of z = 5 = .9999997129.<BR>\n" );
document.write( "area to the right of z = 5 = 1 - .9999997129 = .000000287195.\r<BR>\n" );
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document.write( "when 3.3 < x < 9, area between those 2 x-values is area to the left of z-score of 9 minus area to the left of z-score of -.7 = .9999997129 minus .2419635782 = .7580361347.\r<BR>\n" );
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document.write( "here's what those values look like on a graph.\r<BR>\n" );
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document.write( "if i did this correctly, your solutions are:\r<BR>\n" );
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document.write( "(a) At least 3.3 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( ".7580\r<BR>\n" );
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document.write( "(b) At most 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( ".0000 = 0\r<BR>\n" );
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document.write( "(c) Between 3.3 percent and 9 percent. (Round the z value to 2 decimal places. Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( ".7580\r<BR>\n" );
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