document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156906>Question 1156906</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a)	Suppose that a civil service examination is designed so that 70% of all persons with an IQ of 90 can pass it. Find the probability that among 14 persons with an IQ of 90 who take the test<BR>\n" );
document.write( "i.	At most 5 will pass.<BR>\n" );
document.write( "ii.	At least 11 will pass.<BR>\n" );
document.write( "iii.	From 8 through 12 will pass<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 #779780 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=779780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <i>i. At most 5 will pass.</i><BR>\n" );
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document.write( "n = 14<BR>\n" );
document.write( "p = 0.70<BR>\n" );
document.write( "q = 0.30<BR>\n" );
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document.write( "MEAN = np = 14(0.70) = 9.8<BR>\n" );
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document.write( "SD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28npq%29 ALIGN=MIDDLE  ALT=\"sqrt%28npq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%2A%280.70%29%2A%280.30%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%2A%280.70%29%2A%280.30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.7146<BR>\n" );
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document.write( "P(X ≤ 5) ---> P(X < 5 + 0.5) ---> P(X < 5.5)<BR>\n" );
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document.write( "Z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285.5+-+9.8%29%2F1.7146 ALIGN=MIDDLE  ALT=\"%285.5+-+9.8%29%2F1.7146\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -2.51<BR>\n" );
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document.write( "On a z-table, -2.51 is equal to 0.0060.  That means the area to the left of the curve is 0.0060.  <b>So, the probability \"at most 5 will pass\" is 0.0060.</b><BR>\n" );
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document.write( "<i>ii. At least 11 will pass.</i><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "n = 14<BR>\n" );
document.write( "p = 0.70<BR>\n" );
document.write( "q = 0.30<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "MEAN = np = 14(0.70) = 9.8<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "SD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28npq%29 ALIGN=MIDDLE  ALT=\"sqrt%28npq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%2A%280.70%29%2A%280.30%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%2A%280.70%29%2A%280.30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.7146<BR>\n" );
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document.write( "P(X ≥ 11) ---> P(X > 11 - 0.5) ---> P(X > 10.5)<BR>\n" );
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document.write( "Z = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810.5+-+9.8%29%2F1.7146 ALIGN=MIDDLE  ALT=\"%2810.5+-+9.8%29%2F1.7146\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.41<BR>\n" );
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document.write( "On a z-table, 0.41 is equal to 0.6591.  That means the area to the right of the curve is 0.3409.  <b>So, the probability \"at least 11 will pass\" is 0.3409.</b><BR>\n" );
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document.write( "<i>iii.	From 8 through 12 will pass.</i><BR>\n" );
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document.write( "n = 14<BR>\n" );
document.write( "p = 0.70<BR>\n" );
document.write( "q = 0.30<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "MEAN = np = 14(0.70) = 9.8<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "SD = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28npq%29 ALIGN=MIDDLE  ALT=\"sqrt%28npq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2814%2A%280.70%29%2A%280.30%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2814%2A%280.70%29%2A%280.30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.7146<BR>\n" );
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document.write( "P(8 ≤ X ≤ 12) ---> P(8 - 0.5 < X < 12 + 0.5) ---> P(7.5 < X < 12.5)<BR>\n" );
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document.write( "Z1 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287.5+-+9.8%29%2F1.7146 ALIGN=MIDDLE  ALT=\"%287.5+-+9.8%29%2F1.7146\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -1.34<BR>\n" );
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document.write( "Z2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812.5+-+9.8%29%2F1.7146 ALIGN=MIDDLE  ALT=\"%2812.5+-+9.8%29%2F1.7146\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.57<BR>\n" );
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document.write( "On a z-table:<BR>\n" );
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document.write( "-1.34 is equal to 0.0901<BR>\n" );
document.write( "1.57 is equal to 0.9418<BR>\n" );
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document.write( "Simply subtract 0.0901 from 0.9418 to get a result of 0.8517. <b>So, the probability \"from 8 through 12 will pass\" is 0.8517.</b> </SPAN>\n" );
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