document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185473>Question 1185473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a procedure yields a binomial distribution with  n=330 trials and the probability of success for one trial is p=0.19, Find the mean for this binomial distribution. (Round answer to one decimal place.) <BR>\n" );
document.write( "μ=62.7<BR>\n" );
document.write( "Find the standard deviation for this distribution.(Round answer to two decimal places.) <BR>\n" );
document.write( "σ=7.13<BR>\n" );
document.write( "Use the range rule of thumb to find the minimum usual value μ-2σ and the maximum usual value μ+2σ.<BR>\n" );
document.write( "Enter answer as an interval using square-brackets only with whole numbers. <BR>\n" );
document.write( "usual values=?<BR>\n" );
document.write( "Find the usual values?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816317 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=816317\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = .19<BR>\n" );
document.write( "q = 1 - 0 = .81<BR>\n" );
document.write( "n = 330 = sample size\r<BR>\n" );
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document.write( "m = n * p = .19 * 330 = 62.7 = mean of the binomial distribution.<BR>\n" );
document.write( "s = square root (n * p * q) = sqrt(330 * .19 * .81) = 7.12649999842 = standard deviation of the binomial distribution.\r<BR>\n" );
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document.write( "range rule of thumbs says:\r<BR>\n" );
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document.write( "68% of the scores are within 1 standard deviation of the mean.<BR>\n" );
document.write( "95% of the scores are within 2 standard deviations of the mean.<BR>\n" );
document.write( "99.7% of the scores are within 3 standard deviations of the mean.\r<BR>\n" );
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document.write( "you are looking at 95% of the scores being within 2 standard deviations of the mean.\r<BR>\n" );
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document.write( "the critical z-score for 95% of the scores being within 2 standard deviations of the mean would be plus of minus 1.96.\r<BR>\n" );
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document.write( "use the z-score formula to find the raw score.\r<BR>\n" );
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document.write( "z-score formula is:\r<BR>\n" );
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document.write( "z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "-1.96 = (x - 62.7) / 7.1265 for the low side.<BR>\n" );
document.write( "1.96 = (x - 62.7) / 7.1265 for the high side.\r<BR>\n" );
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document.write( "solve for x in each to get:\r<BR>\n" );
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document.write( "x = -1.96 * 7.1265 + 62.7 = 48.73206 for the low side.<BR>\n" );
document.write( "x = 1.96 * 7.1265 + 62.7 = 76.66794 for the high side.\r<BR>\n" );
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document.write( "the scores with 95% of the normal distribution between them would be 48.73206 to 76.66794.\r<BR>\n" );
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document.write( "if you round to the nearest integer, you get 49 to 77.\r<BR>\n" );
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document.write( "in interval notation that would be [49,77].\r<BR>\n" );
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document.write( "i don't know what is meant by usual values.<BR>\n" );
document.write( "i think the above is your answer.<BR>\n" );
document.write( "give it a whirl; see how you do.\r<BR>\n" );
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document.write( "here's a reference on binomial distribution.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://stattrek.com/probability-distributions/binomial.aspx\" target = \"_blank\">https://stattrek.com/probability-distributions/binomial.aspx</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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