document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174294>Question 1174294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let X be a random variable normally distributed with parameters μ= 70, σ= 10. Estimate P(65<X<85).<BR>\n" );
document.write( "(Give the probability in the form of a decimal number (example: 0.123)!\r<BR>\n" );
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document.write( "This is the question that I have and I have done it this way.<BR>\n" );
document.write( "P8(65<X<85) = P(X<85) - P(X<65)<BR>\n" );
document.write( "Z(85) = (85-70)/10 = 1.5<BR>\n" );
document.write( "P(X<85) = 0.066807\r<BR>\n" );
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document.write( "Z(65) = (65-70)/10 = -0.5\r<BR>\n" );
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document.write( "However, I am not quite sure how I get P, I used an online calculator, and in the results it should be 0.624<BR>\n" );
document.write( "> pnorm(85,70,10)-pnorm(65,70,10)=0.6246553\r<BR>\n" );
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document.write( "Can someone explain this to me? Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799715 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your mean is 70 and your standard deviation is 10.<BR>\n" );
document.write( "you want to know the probability of getting a score between 65 and 85 if i understand you correctly.\r<BR>\n" );
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document.write( "using my ti-85 plus calculator, i got the same probability that you did as .6246553.\r<BR>\n" );
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document.write( "if you use the normal distribution tables, you would do the following.\r<BR>\n" );
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document.write( "first you want to find the z-score for 65 and 85 with a mean of 70 and a standard deviation of 10\r<BR>\n" );
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document.write( "the z-score formula is:<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "for x = 65, this formula becomes z = (65 - 70) / 10 = 1.5<BR>\n" );
document.write( "for x = 85, this formula becomes z = (85 - 70) / 10 = -.5\r<BR>\n" );
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document.write( "you go to the z-score table to find the area to the left of 1.5 and the area to the left of -.5.<BR>\n" );
document.write( "you will get area to the left of z-score of -.5 = .30854 and area to the left of z-score of 1.5 = .93319.<BR>\n" );
document.write( "subtract the smaller area from the larger area to get .62465.\r<BR>\n" );
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document.write( "if you round to 3 decimal, the calculator gets you .625 and the table gets you .625.\r<BR>\n" );
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document.write( "if you truncate to 3 decimal places, you will get .624.\r<BR>\n" );
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document.write( "your calculator results of .6246553 will be equal to .625 when you round to 3 decimal places.\r<BR>\n" );
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document.write( "outside of the rounding discrepancy, the results i gave you pretty much agree with what your calculator gave you.\r<BR>\n" );
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document.write( "if i rounded .93319 to 3 decimal places, it would be equal to .933.<BR>\n" );
document.write( "if i rounded .30854 to 3 decimal places, it would be equal to .309.<BR>\n" );
document.write( "subtract .309 from .933 and you will get .624.\r<BR>\n" );
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document.write( "if you used the stattrek online calculator, that calculator rounds the probability to 3 decimal places.<BR>\n" );
document.write( "that would explain the discrepancy.\r<BR>\n" );
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document.write( "the table i used can be found at <a  rel=nofollow HREF= \"https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf\" target = \"_blank\">https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf</a>\r<BR>\n" );
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document.write( "let me know if this answers your question and whether this is enough for you to understand how to do it.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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