document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190385>Question 1190385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assuming the normal heart rate (H.R) in normal healthy individuals is normally distributed with<BR>\n" );
document.write( "Mean = 70 and Standard Deviation =10 beats/min.<BR>\n" );
document.write( "a) What is the probability that the heart rate is above 80 beats/min?<BR>\n" );
document.write( "b) What is the probability that the heart rate is above 90 beats/min?<BR>\n" );
document.write( "c) What is the probability that the heart rate is between 50-90 beats/min?<BR>\n" );
document.write( "d) What is the probability that the heart rate is above 100 beats/min? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822008 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=822008\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "mu = 70 = population mean<BR>\n" );
document.write( "sigma = 10 = population standard deviation\r<BR>\n" );
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document.write( "Convert x = 80 to its corresponding z score<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (80-70)/10<BR>\n" );
document.write( "z = 10/10<BR>\n" );
document.write( "z = 1\r<BR>\n" );
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document.write( "The question of asking P(X > 80) is identical to P(Z > 1) when we have the parameters of mu = 70 and sigma = 10.\r<BR>\n" );
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document.write( "Use a Z table in the back of your textbook to find that <BR>\n" );
document.write( "P(Z < 1) = 0.84134\r<BR>\n" );
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document.write( "Here's a free Z table if you don't have your stats textbook with you<BR>\n" );
document.write( "https://www.ztable.net/\r<BR>\n" );
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document.write( "From that we could say:<BR>\n" );
document.write( "P(Z > 1) = 1 - P(Z < 1)<BR>\n" );
document.write( "P(Z > 1) = 1 - 0.84134<BR>\n" );
document.write( "P(Z > 1) = 0.15866\r<BR>\n" );
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document.write( "Answer: Approximately 0.15866\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "You'll follow the same steps as the previous part.<BR>\n" );
document.write( "x = 90 converts to z = 2. I'm skipping steps a bit.<BR>\n" );
document.write( "P(X > 90) is equivalent to P(Z > 2)\r<BR>\n" );
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document.write( "Use the table to find that<BR>\n" );
document.write( "P(Z < 2) = 0.97725<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "P(Z > 2) = 1 - P(Z < 2)<BR>\n" );
document.write( "P(Z > 2) = 1 - 0.97725<BR>\n" );
document.write( "P(Z > 2) = 0.02275\r<BR>\n" );
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document.write( "Answer: Approximately 0.02275\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "x = 50 converts to z = -2<BR>\n" );
document.write( "x = 90 converts to z = 2\r<BR>\n" );
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document.write( "Computing P(50 < X < 90) is equivalent to P(-2 < Z < 2)\r<BR>\n" );
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document.write( "The table shows that<BR>\n" );
document.write( "P(Z < -2) = 0.02275<BR>\n" );
document.write( "P(Z < 2) = 0.97725\r<BR>\n" );
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document.write( "This leads to:<BR>\n" );
document.write( "P(a < Z < b) = P(Z < b) - P(Z < a)<BR>\n" );
document.write( "P(-2 < Z < 2) = P(Z < 2) - P(Z < -2)<BR>\n" );
document.write( "P(-2 < Z < 2) = 0.97725 - 0.02275<BR>\n" );
document.write( "P(-2 < Z < 2) = 0.9545<BR>\n" );
document.write( "This fits with the Empirical Rule which says roughly 95% of the normal distribution is within 2 standard deviations of the mean.\r<BR>\n" );
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document.write( "Answer: Approximately 0.9545\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "x = 100 converts to z = 3<BR>\n" );
document.write( "P(Z < 3) = 0.99865<BR>\n" );
document.write( "P(Z > 3) = 1 - P(Z < 3)<BR>\n" );
document.write( "P(Z > 3) = 1 - 0.99865<BR>\n" );
document.write( "P(Z > 3) = 0.00135\r<BR>\n" );
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document.write( "Answer: Approximately 0.00135\r<BR>\n" );
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document.write( "You can use a normalCDF calculator to compute the more accurate versions of each approximate answer above.<BR>\n" );
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