document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199907>Question 1199907</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 66% of all violent felons in the prison system are repeat offenders. If 45 violent felons are randomly selected, find the probability that<BR>\n" );
document.write( "( I just need help on letter C, the rest I got them correct)<BR>\n" );
document.write( "a. Exactly 29 of them are repeat offenders. <BR>\n" );
document.write( "0.1205286384<BR>\n" );
document.write( "Correct\r<BR>\n" );
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document.write( "b. At most 29 of them are repeat offenders. <BR>\n" );
document.write( "0.4682375156<BR>\n" );
document.write( "Correct\r<BR>\n" );
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document.write( "c. At least 30 of them are repeat offenders. ?\r<BR>\n" );
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document.write( "d. Between 27 and 31 (including 27 and 31) of them are repeat offenders.<BR>\n" );
document.write( "0.553313931<BR>\n" );
document.write( "Correct </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833887 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=833887\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll focus on part (c) only.\r<BR>\n" );
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document.write( "For questions like this, you could calculate by hand. <BR>\n" );
document.write( "However that is tedious busy-work in my opinion. The reason why I say this is because you would have 16 separate calculations, each of which are somewhat long in their own right.\r<BR>\n" );
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document.write( "It's better to use a specialized binomial distribution calculator such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.gigacalculator.com/calculators/binomial-probability-calculator.php\">https://www.gigacalculator.com/calculators/binomial-probability-calculator.php</a><BR>\n" );
document.write( "In this case:<BR>\n" );
document.write( "n = 45 = sample size<BR>\n" );
document.write( "p = 0.66 = probability of a repeat offender<BR>\n" );
document.write( "x = 30 = number of repeat offenders<BR>\n" );
document.write( "Look for where it says \"Probability of X ≥ 30 events\".\r<BR>\n" );
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document.write( "If you want to use your TI83 or TI84 calculator, then refer to this page for more information<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.statology.org/binomial-probabilities-ti-84-calculator/\">https://www.statology.org/binomial-probabilities-ti-84-calculator/</a><BR>\n" );
document.write( "Focus on the binomialcdf function and NOT the binomialpdf.<BR>\n" );
document.write( "That page explains how to find the binomialcdf function. Also there are examples.\r<BR>\n" );
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document.write( "Something like <BR>\n" );
document.write( "binomialcdf(45,0.66,29)<BR>\n" );
document.write( "will calculate the sum of the probability values from x = 0 to x = 29\r<BR>\n" );
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document.write( "Subtract that from 1 to find the sum of the probabilities from x = 30 to x = 45.\r<BR>\n" );
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document.write( "This is valid because<BR>\n" );
document.write( "P(0 ≤ X ≤ 29) + P(30 ≤ X ≤ 45) = 1 \r<BR>\n" );
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document.write( "Therefore you'll type into the TI83 or TI84 calculator <font color=red>1-binomialcdf(45,0.66,29)</font> to find the probability of having at least 30 repeat offenders.<BR>\n" );
document.write( "Be careful to avoid typing in 1-binomialcdf(45,0.66,30) as that would slightly be off.\r<BR>\n" );
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document.write( "If instead you want to use a spreadsheet, then the command is called BINOMDIST<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://support.microsoft.com/en-us/office/binomdist-function-506a663e-c4ca-428d-b9a8-05583d68789c\">https://support.microsoft.com/en-us/office/binomdist-function-506a663e-c4ca-428d-b9a8-05583d68789c</a>\r<BR>\n" );
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document.write( "There are many other options.\r<BR>\n" );
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document.write( "Let me know if you have any questions about a particular piece of software, website, spreadsheet, or calculator. \r<BR>\n" );
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document.write( "Hint about the final answer: It is between 0.5 and 0.6<BR>\n" );
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