document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191928>Question 1191928</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for a normal distribution if the value of mean is 70 and standard deviation is 15.75 find the points<BR>\n" );
document.write( "(a) in which it contains 98% area between them<BR>\n" );
document.write( "(b) in which it contains 95% area between them<BR>\n" );
document.write( "(c) in which it contains 85% area between them<BR>\n" );
document.write( "(d) in which 60% area between them<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 #823807 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=823807\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "Your teacher is asking you to find the values of m and n such that<BR>\n" );
document.write( "P(m < X < n) = 0.98<BR>\n" );
document.write( "The problem is that there are infinitely many solutions for m,n.\r<BR>\n" );
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document.write( "It's similar to how<BR>\n" );
document.write( "P(r < Z < s) = 0.98<BR>\n" );
document.write( "also has infinitely many solutions for r,s\r<BR>\n" );
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document.write( "However, if we were to use symmetry and say<BR>\n" );
document.write( "P(-k < Z < k) = 0.98<BR>\n" );
document.write( "then there's exactly one solution for k\r<BR>\n" );
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document.write( "For the duration of this solution, I'll assume that your teacher is using the P(-k < Z < k) method.\r<BR>\n" );
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document.write( "98% of the area is in the main body leaving 100% - 98% = 2% in the two tails combined. <BR>\n" );
document.write( "Each tail would have (2%)/2 = 1% of the area. <BR>\n" );
document.write( "We're able to divide by two because of the mirror symmetry mentioned.\r<BR>\n" );
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document.write( "Use a table or calculator to find that P(Z < k) = 0.01 has a solution of roughly k = -2.327<BR>\n" );
document.write( "Here's a useful calculator<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://davidmlane.com/normal.html\">https://davidmlane.com/normal.html</a>\r<BR>\n" );
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document.write( "That k value leads to<BR>\n" );
document.write( "P(-2.327 < Z < 2.327) = 0.98<BR>\n" );
document.write( "Meaning that about 98% of the area under the standard normal Z curve is between the z scores -2.327 and 2.327\r<BR>\n" );
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document.write( "Now let's convert each mentioned z score into their corresponding raw score.\r<BR>\n" );
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document.write( "We'll start with z = -2.327<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z*sigma = x-mu<BR>\n" );
document.write( "x = mu+z*sigma<BR>\n" );
document.write( "x = 70+(-2.327)*15.75<BR>\n" );
document.write( "x = 33.34975\r<BR>\n" );
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document.write( "Then repeat for z = 2.327<BR>\n" );
document.write( "x = mu+z*sigma<BR>\n" );
document.write( "x = 70+2.327*15.75<BR>\n" );
document.write( "x = 106.65025\r<BR>\n" );
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document.write( "Therefore,<BR>\n" );
document.write( "P(33.34975 < X < 106.65025) = 0.98<BR>\n" );
document.write( "approximately\r<BR>\n" );
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document.write( "You'll follow similar steps for parts (b) through (d).<BR>\n" );
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