document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=285960>Question 285960</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed.\r<BR>\n" );
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document.write( "a) What is the probability a company will have a stock price of at least $40?<BR>\n" );
document.write( "b) What is the probability a company will have a stock price no higher than $20?<BR>\n" );
document.write( "c) How high does a stock price have to be to put a company in the top 10%?\r<BR>\n" );
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document.write( "I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says \"at least\" or \"no higher than\" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207357 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=207357\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed. <BR>\n" );
document.write( "a) What is the probability a company will have a stock price of at least $40?<BR>\n" );
document.write( "Find the z-score of 40.<BR>\n" );
document.write( "Formula: z(x) = (x-u)/s<BR>\n" );
document.write( "z(40) = (40-30)/8.2 = 1.2195<BR>\n" );
document.write( "Note: That means 40 is 1.2195 standard deviations above the mean.<BR>\n" );
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document.write( "Having converted 40 to a z-score you find the <BR>\n" );
document.write( "area to the right of 1.2195 under the standard curve.<BR>\n" );
document.write( "P(x> 40) = P(z> 1.2195)<BR>\n" );
document.write( "You have to use technology or a z-chart to find the<BR>\n" );
document.write( "area to the right of 1.2195.<BR>\n" );
document.write( "I use a TI84 calculator and get normalcdf(1.2195,100) = 0.1113..<BR>\n" );
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document.write( "b) What is the probability a company will have a stock price no higher than $20?<BR>\n" );
document.write( "z(20) = (20-30)/8.2 = -1.2295<BR>\n" );
document.write( "Note: Here you are finding the area to the left of -1.2295.<BR>\n" );
document.write( "Because of symmetry the answer is the same as for \"a\".<BR>\n" );
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document.write( "c) How high does a stock price have to be to put a company in the top 10%?<BR>\n" );
document.write( "Find the z-score that has a right tail of 10%.<BR>\n" );
document.write( "I use the TI to get invNorm(0.90) = 1.28155..<BR>\n" );
document.write( "Use the formula x = zs + u<BR>\n" );
document.write( "x = 1.28155*8.2 + 30<BR>\n" );
document.write( "x = $40.51<BR>\n" );
document.write( "Stock prices above $40.51 are in the top 10% of the stock prices.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "I'm sure I could work through a and b if I knew how to set up the equation? I'm really struggling to understand my current stats teacher, our whole class is. I just don't know where to start when it says \"at least\" or \"no higher than\" I don't know what number to use.....and letter c has me at a total loss. Thank you so much in advance for your help! If possible, can you show the equations you use so I have a starting point for future problems - and could show the rest of my class? Thanks again!!<BR>\n" );
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