document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208601>Question 1208601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mail Order A mail order company has a 6% success rate. If it mails advertisements to 525 people, find the probability of getting less than 27 sales. Use The Standard Normal Distribution Table. Round z-value calculations to 2 decimal places and final answer to at least 4 decimal places.\r<BR>\n" );
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document.write( "P(X<27)= </SPAN>\n" );
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document.write( "Answer: <font color=red>0.17879</font>\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "We have a binomial distribution with these parameters<BR>\n" );
document.write( "n = 525 = sample size<BR>\n" );
document.write( "p = 0.06 = probability of success\r<BR>\n" );
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document.write( "To ensure we can use a normal distribution to approximate this binomial distribution, we must check that n*p > 5 and n*(1-p) > 5<BR>\n" );
document.write( "n*p = 525*0.06 = 31.5<BR>\n" );
document.write( "n*(1-p) = 525*(1-0.06) = 493.5<BR>\n" );
document.write( "Both results exceed 5, so the requirements are met.<BR>\n" );
document.write( "Some textbooks will raise the threshold to n*p > 10 and n*(1-p) > 10. The results also meet these requirements.\r<BR>\n" );
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document.write( "mu = n*p = 525*0.06 = 31.5 is the mean<BR>\n" );
document.write( "sigma = sqrt(n*p*(1-p)) = sqrt(525*0.06*(1-0.06)) = 5.44150714 is the approximate standard deviation\r<BR>\n" );
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document.write( "Using a <a  rel=nofollow HREF=\"https://www.statisticshowto.com/what-is-the-continuity-correction-factor/\">continuity correction factor</a>, we'll adjust P(X < 27) to get P(X < 26.5)\r<BR>\n" );
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document.write( "Compute the z score.<BR>\n" );
document.write( "z = (x - mu)/sigma<BR>\n" );
document.write( "z = (26.5 - 31.5)/5.44150714<BR>\n" );
document.write( "z = -0.91886307807<BR>\n" );
document.write( "z = -0.92 is the approximate z score when rounding to 2 decimal places.\r<BR>\n" );
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document.write( "Then use the <a  rel=nofollow HREF=\"https://www.ztable.net/\">Standard Normal Distribution Table</a> (also known as Z table) that your teacher has provided you.<BR>\n" );
document.write( "Usually such a table is found in the back of your stats textbook.\r<BR>\n" );
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document.write( "Locate the row that starts with -0.9<BR>\n" );
document.write( "Highlight the column that has 0.02 at the top.<BR>\n" );
document.write( "The value <font color=red>0.17879</font> is in this row and column. <BR>\n" );
document.write( "This value is approximate.<BR>\n" );
document.write( "We can say that P(Z < -0.92) = <font color=red>0.17879</font> which is the approximate final answer in decimal form.<BR>\n" );
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