document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199362>Question 1199362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible.\r<BR>\n" );
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document.write( "a. What is the distribution of X? X ~ N(64, 2.3)\r<BR>\n" );
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document.write( "b. Find the probability that the person is between 61.9 and 63.3 inches. <BR>\n" );
document.write( "0.1998\r<BR>\n" );
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document.write( "c. The middle 20% of Martian heights lie between what two numbers?<BR>\n" );
document.write( "Low: <BR>\n" );
document.write( " inches<BR>\n" );
document.write( "High: <BR>\n" );
document.write( " inches\r<BR>\n" );
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document.write( "How do I solve letter C? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833215 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52800)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833215\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "Middle &nbsp;20% &nbsp;are those who are lower than upper &nbsp;60% &nbsp;and higher than lower 40%.\r<BR>\n" );
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document.write( "Use your calculator &nbsp;TI-83 or &nbsp;TI-84 &nbsp;with &nbsp;function &nbsp;&nbsp;invNorm.\r<BR>\n" );
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document.write( "Its format is &nbsp;&nbsp;p = invNorm ( probability, mu, SD).\r<BR>\n" );
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document.write( "For details and instructions about this function and how to use it, &nbsp;see web-site \r<BR>\n" );
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document.write( "https://www.statology.org/invnorm-ti-84/   \r<BR>\n" );
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document.write( "The &nbsp;z-scores are\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;z_lower_40% = invNorm(0.4, 64, 2.3) = 63.4173.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;z_upper_60% = invNorm(0.6, 64, 2.3) =  64.5827.\r<BR>\n" );
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document.write( "<U>ANSWER</U>.  &nbsp;&nbsp;&nbsp;&nbsp;The middle &nbsp;20% &nbsp;of &nbsp;Martian heights lie between  &nbsp;63.42 &nbsp;and &nbsp;64.58 inches &nbsp;&nbsp;(after rounding).\r<BR>\n" );
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document.write( "-------------------\r<BR>\n" );
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document.write( "You may also use online calculator https://onlinestatbook.com/2/calculators/inverse_normal_dist.html\r<BR>\n" );
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document.write( "It has several advantages: \r<BR>\n" );
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document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- it is free of charge; <BR>\n" );
document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- it has simple and intuitively clear interface, and <BR>\n" );
document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- it shows you the shaded area of interest, so at any time moment you can see and understand <BR>\n" );
document.write( "    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;what you are doing, what you are doing wrong &nbsp;(if any) &nbsp;and how to do it right.\r<BR>\n" );
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document.write( "Play with this online calculator and use it in different modes until everything will become clear to you.\r<BR>\n" );
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document.write( "This online calculator is the best tool to learn about the normal distribution <BR>\n" );
document.write( "and to learn on how to work with normal distribution, making necessary calculations.\r<BR>\n" );
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document.write( "So, this online calculator is your best teacher, best assistant and your <BR>\n" );
document.write( "best friend when you calculate something related to normal distribution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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