document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204348>Question 1204348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean price of new homes from a sample of houses is $165,000 with a standard deviation of $21,000. The data set has a bell-shaped distribution. Between what two do 95% of the houses fall? \r<BR>\n" );
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document.write( "Using the sample statistics from above, find the z-scores of each of the following house prices. \r<BR>\n" );
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document.write( "a. $202,000<BR>\n" );
document.write( "b. $70,000<BR>\n" );
document.write( "c. $175,000<BR>\n" );
document.write( "d. $137,000 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840546 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=840546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll leave problem 1 for the student to do.<BR>\n" );
document.write( "Hint: The value 1.96 is involved somehow.\r<BR>\n" );
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document.write( "I'll focus on part (a) of the 2nd question.\r<BR>\n" );
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document.write( "Since every value is in thousands, we can ignore the trailing triple zeros at the end. They'll cancel out anyway.<BR>\n" );
document.write( "For example, think of $202,000 as just 202.\r<BR>\n" );
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document.write( "Let's compute the z score<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (202 - 165)/21<BR>\n" );
document.write( "z = 1.76190476190477<BR>\n" );
document.write( "z = 1.76<BR>\n" );
document.write( "This is the approximate number of standard deviation units that we are above the mean.\r<BR>\n" );
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document.write( "In many Z tables, perhaps all of them(?), it's customary that the z scores are rounded to two decimal places.<BR>\n" );
document.write( "Here's an example of one such table<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.ztable.net/\">https://www.ztable.net/</a>\r<BR>\n" );
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document.write( "The calculations for parts (b) through (d) will follow the same template of steps.<BR>\n" );
document.write( "Please let me know if you have questions about any of the steps shown above.<BR>\n" );
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