document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878456>Question 878456</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having a hard time understanding how to compute this question. I'm just starting my summer school class and my teacher is absolutely HORRID! It's his first time ever teaching and he doesn't speak english well! \r<BR>\n" );
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document.write( "My question is how do I solve this question?<BR>\n" );
document.write( "Question:\r<BR>\n" );
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document.write( "SunBlush Technologies tracks their daily profits and has found that the distribution of profits is approximately normal with a mean of $21,900.00 and a standard deviation of about $500.00. Using this information, answer the following questions. Round your intermediate answers (z-values) to 2 decimal places in order to be able to read the corresponding area values from the table.<BR>\n" );
document.write( "For full marks your answer should be accurate to at least four decimal places.\r<BR>\n" );
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document.write( "Compute the probability that tomorrow's profit will be:\r<BR>\n" );
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document.write( "a) between $20,580.00 and $21,405.00   <BR>\n" );
document.write( "b) less than $22,615.00 or greater than $23,085.00   <BR>\n" );
document.write( "c) less than $22,455.00   <BR>\n" );
document.write( "d) between $20,525.00 and $22,785.00<BR>\n" );
document.write( "e) between $22,825.00 and $23,335.00   <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 #529963 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=529963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For this entire problem, I'm using <a  rel=nofollow HREF=\"http://www.math.upenn.edu/~chhays/zscoretable.pdf\">this table</a>\r<BR>\n" );
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document.write( "a)\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 20580\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (20580 - 21900)/500<BR>\n" );
document.write( "z = -2.64\r<BR>\n" );
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document.write( "Use the table (mentioned above) to find that the area to the left of z = -2.64 is 0.0041\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 21405\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (21405 - 21900)/500<BR>\n" );
document.write( "z = -0.99\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = -0.99 is 0.1611\r<BR>\n" );
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document.write( "Subtract the two areas: 0.1611 - 0.0041 = 0.1570\r<BR>\n" );
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document.write( "The area between z = -2.64 and z = -0.99 is 0.1570<BR>\n" );
document.write( "The area between x = 20580 and x = 21405 is 0.1570<BR>\n" );
document.write( "The two areas are the same because we applied a z-score transform.\r<BR>\n" );
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document.write( "That means the probability of being between $20,580.00 and $21,405.00 is <font color=\"red\">0.1570</font>\r<BR>\n" );
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document.write( "b)\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 22615\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (22615 - 21900)/500<BR>\n" );
document.write( "z = 1.43\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = 1.43 is 0.9236\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 23085\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (23085 - 21900)/500<BR>\n" );
document.write( "z = 2.37\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = 2.37 is 0.9911<BR>\n" );
document.write( "Subtract that from 1 to get 1-0.9911 = 0.0089<BR>\n" );
document.write( "The area to the right of z = 2.37 is 0.0089\r<BR>\n" );
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document.write( "Add the two areas: 0.9236+0.0089 = 0.9325\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">0.9325</font>\r<BR>\n" );
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document.write( "c)\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 22455\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (22455 - 21900)/500<BR>\n" );
document.write( "z = 1.11\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = 1.11 is 0.8665\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">0.8665</font>\r<BR>\n" );
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document.write( "d)\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 20525\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (20525 - 21900)/500<BR>\n" );
document.write( "z = -2.75\r<BR>\n" );
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document.write( "Use the table (mentioned above) to find that the area to the left of z = -2.75 is 0.0030\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 22785\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (22785 - 21900)/500<BR>\n" );
document.write( "z = 1.77\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = 1.77 is 0.9616\r<BR>\n" );
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document.write( "Subtract the two areas: 0.9616 - 0.0030 = 0.9586\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">0.9586</font>\r<BR>\n" );
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document.write( "e)\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 22825\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (22825 - 21900)/500<BR>\n" );
document.write( "z = 1.85\r<BR>\n" );
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document.write( "Use the table (mentioned above) to find that the area to the left of z = 1.85 is 0.9678\r<BR>\n" );
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document.write( "Compute the z-score when the raw score is x = 23335\r<BR>\n" );
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document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (23335 - 21900)/500<BR>\n" );
document.write( "z = 2.87\r<BR>\n" );
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document.write( "Use the table to find that the area to the left of z = 2.87 is 0.9979\r<BR>\n" );
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document.write( "Subtract the two areas: 0.9979 - 0.9678 = 0.0301\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">0.0301</font> </SPAN>\n" );
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