document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75466>Question 75466</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q1. A final exam in math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test score is greater than 78.\r<BR>\n" );
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document.write( "Q2.For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 16 and p = 0.5\r<BR>\n" );
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document.write( "Q3. This is the same as question 1, but find the probability that the mean of their test scores is LESS than 70\r<BR>\n" );
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document.write( "Q4. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. With n = 20 and p = 0.06, estimate p (fewer than 8). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54160 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=54160\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Q1. A final exam in math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test score is greater than 78.<BR>\n" );
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document.write( "z(78)=(78-73)/7.8/sqrt(24)=3.14<BR>\n" );
document.write( "P(z>3.14)=0.0008448059....<BR>\n" );
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document.write( "Q2.For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. n = 16 and p = 0.5<BR>\n" );
document.write( "The answer to this depends on the conditions listed in your text for using<BR>\n" );
document.write( "a normal approximation on a binomial problem. <BR>\n" );
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document.write( "Q3. This is the same as question 1, but find the probability that the mean of their test scores is LESS than 70<BR>\n" );
document.write( "z(70)=(70-73)/7.8/sqrt(24)=-1.88442228...<BR>\n" );
document.write( "P(z<-1.88442228...)=0.02975...<BR>\n" );
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document.write( "Q4. Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. With n = 20 and p = 0.06, estimate <BR>\n" );
document.write( "P(fewer than 8).<BR>\n" );
document.write( "Z(8)=(8-20*0.06)/sqrt(20*0.06*0.94)=6.8/1.06207=6.40257<BR>\n" );
document.write( "P(z<6.40257)=0.9999<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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