document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=227729>Question 227729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,<BR>\n" );
document.write( "Would someone be able to help me with this statistics homework problem?\r<BR>\n" );
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document.write( ">Determine the following normal probabilities.  Assume that, among residents of a large Florida subdivision, the population mean age is 65 years old, the population standard deviation is 2 years, and that the age variable is distributed normally.  \r<BR>\n" );
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document.write( "1.What is the probability that a randomly chosen individual would be between 62 and 67 years of age?  Draw a graph.\r<BR>\n" );
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document.write( "2.What is the probability that a randomly chosen individual would be less than 64 years of age?  \r<BR>\n" );
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document.write( "3.What is the probability that a randomly chosen individual would be either less than 64 years of age or more than 66 years of age?  \r<BR>\n" );
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document.write( "4.Find the specific age for which the following statement is true:  The probability of being this age, or older, is 20%.  \r<BR>\n" );
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document.write( "Thank you for your time,\r<BR>\n" );
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document.write( "Rob\r<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 #169203 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=169203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the following normal probabilities. Assume that, among residents of a large Florida subdivision, the population mean age is 65 years old, the population standard deviation is 2 years, and that the age variable is distributed normally.<BR>\n" );
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document.write( "You need to be able to find z-scores with a calculator or by <BR>\n" );
document.write( "using a z-chart to work these problems.<BR>\n" );
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document.write( "1.What is the probability that a randomly chosen individual would be between 62 and 67 years of age? Draw a graph.<BR>\n" );
document.write( "z(62) = (62-65)/2 = -1.5<BR>\n" );
document.write( "z(67) = (67-65)2 = 1<BR>\n" );
document.write( "P(62 < x < 67) = P(-1.5 < z < 1) = 0.7745<BR>\n" );
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document.write( "2.What is the probability that a randomly chosen individual would be less than 64 years of age?<BR>\n" );
document.write( "z(64)= (64-65)/2 = -1/2<BR>\n" );
document.write( "P(x < 64) = P(z < -1/2) = 0.3085<BR>\n" );
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document.write( "3.What is the probability that a randomly chosen individual would be either less than 64 years of age or more than 66 years of age?<BR>\n" );
document.write( "z(64) = -1/2<BR>\n" );
document.write( "z(66) = (66-65)/2 = 1/2 <BR>\n" );
document.write( "P(x < 64 or x > 65) = P(z < -1/2 or x > 1/2 = P(z < -1/2) + P(z > 1/2)<BR>\n" );
document.write( "= 0.3085 + 0.3085 = 0.6171<BR>\n" );
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document.write( "4.Find the specific age for which the following statement is true: The probability of being this age, or older, is 20%.<BR>\n" );
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document.write( "Find the z-value which has 20% of the population to the right:<BR>\n" );
document.write( "That value is invNorm(0.80) = 0.8416<BR>\n" );
document.write( "Now use x = zs +u to find the corresponding raw score.<BR>\n" );
document.write( "x = 0.8416*2 + 65 <BR>\n" );
document.write( "x = 66.6832 (Prob of being this age or older is 20%)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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