document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=685934>Question 685934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a normal distribution with µ = 100 and &#963; = 10, if you select a sample of n = 25, what is the probability that x¯ is:<BR>\n" );
document.write( "a. less than 47?<BR>\n" );
document.write( "b. between 95 and 97.5?<BR>\n" );
document.write( "c. above 102.2?<BR>\n" );
document.write( "d. there is a 65% chance that x¯ is above what value? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #424667 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=424667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given a normal distribution with µ = 100 and &#963; = 10, if you select a sample of n = 25, what is the probability that x-bar is:<BR>\n" );
document.write( "a. less than 47?<BR>\n" );
document.write( "z(47) = (47-100)/[10/sqrt(25)] = -52/2 = -26<BR>\n" );
document.write( "P(x-bar < 47) = P(z < -26) is very close to zero.<BR>\n" );
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document.write( "b. between 95 and 97.5?<BR>\n" );
document.write( "Find the z-value corresponding to 95 and 97.57<BR>\n" );
document.write( "Find the Probability between those z values.<BR>\n" );
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document.write( "c. above 102.2?<BR>\n" );
document.write( "Find the z-value of 102.2<BR>\n" );
document.write( "Find the probability that z is above that z-value.<BR>\n" );
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document.write( "d. there is a 65% chance that x-bar is above what value?<BR>\n" );
document.write( "Find the z-value with a left tail of 0.35<BR>\n" );
document.write( "invNorm(0.35) = -0.3853<BR>\n" );
document.write( "Find the x-bar value using x-bar = z*s + u<BR>\n" );
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document.write( "x-bar = -0.3853*2+100 = 99.23<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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