document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178586>Question 1178586</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Let the random variable X follow a normal distribution with 𝜇= 80 and 𝜎2= 100. a.Find the probability that X is greater than 60. Draw a probability distribution graph.b. Find the probability that X is greater than 72 and less than 82.c. Find the probability that X is less than 55.d. The probability is 0.1 that X is greater than what number? e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?<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 #807907 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=807907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this online calculator makes the solution to these problem easy.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "it is based on z-scores.\r<BR>\n" );
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document.write( "the answer to your problems are shown below:\r<BR>\n" );
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document.write( "in these problems, the mean is 80 and the standard deviation is equal to the square root of the variance = sqrt(100) = 10.\r<BR>\n" );
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document.write( "a. Find the probability that X is greater than 60. Draw a probability distribution graph. \r<BR>\n" );
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document.write( "b. Find the probability that X is greater than 72 and less than 82.\r<BR>\n" );
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document.write( "c. Find the probability that X is less than 55.\r<BR>\n" );
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document.write( "d. The probability is 0.1 that X is greater than what number? \r<BR>\n" );
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document.write( "e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?\r<BR>\n" );
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document.write( "the calculator is very simple to use.<BR>\n" );
document.write( "the main thing you have to do is to calculate the standard deviation or the standard error correctly.\r<BR>\n" );
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document.write( "in this problem, the standard deviation of the population is used.<BR>\n" );
document.write( "since the standard deviation is the square root of the variance, then the standard deviation in this problem is square root of 100 = 10.\r<BR>\n" );
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document.write( "if you're dealing with a sample of the population of a certain size, then the standard error is used.\r<BR>\n" );
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document.write( "the formula for that is standard error = standard deviation / square root of sample size.\r<BR>\n" );
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document.write( "if you have to work with z-scores, the same calculator can be used.<BR>\n" );
document.write( "in that case, the mean is 0 and the standard deviation is 1.\r<BR>\n" );
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document.write( "if you have any questions about that you still need to answer, let me know.\r<BR>\n" );
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document.write( "theo </SPAN>\n" );
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