document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=385745>Question 385745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A set of final examination grades in an introductory statistics course was founded to be normally distributed with a mean of 73 and a standard deviation of 8.\r<BR>\n" );
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document.write( "a. what is the probability of getting at most a grade of 91 on the exam?<BR>\n" );
document.write( "b. what percentage of students scored between 65 and 85?<BR>\n" );
document.write( "c. what percentage of students scored between81 and 89?<BR>\n" );
document.write( "d. what is the final exam grade in only 5% of the students taking the test scored higher?<BR>\n" );
document.write( "e. If the professor \"curves\"( gives A`s to the top 10% of the class regardless of the score), are you better off with a grade of 81on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? show statistically and explain<BR>\n" );
document.write( " Include a normal distribution curve </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272880 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=272880\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A set of final examination grades in an introductory statistics course was founded to be normally distributed with a mean of 73 and a standard deviation of 8. <BR>\n" );
document.write( "a. what is the probability of getting at most a grade of 91 on the exam?<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(91) = (91-73)/8 = 2.25<BR>\n" );
document.write( "P(x <= 91) = P(z < 2.25) = 0.9878<BR>\n" );
document.write( "------------------------------------------------------- <BR>\n" );
document.write( "b. what percentage of students scored between 65 and 85?<BR>\n" );
document.write( "P(65 < x < 85) = 0.7745<BR>\n" );
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document.write( "c. what percentage of students scored between81 and 89?<BR>\n" );
document.write( "P(81< x <89) = 0.1359<BR>\n" );
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document.write( "d. what is the final exam grade if only 5% of the students taking the test scored higher?<BR>\n" );
document.write( "Find the z-value with a right tail of 5%: z = 1.645<BR>\n" );
document.write( "Find the corresponding exam score:<BR>\n" );
document.write( "x = zs+u<BR>\n" );
document.write( "x = 1.645*8+73<BR>\n" );
document.write( "x = 86.16<BR>\n" );
document.write( "=============<BR>\n" );
document.write( "e. If the professor \"curves\"( gives A`s to the top 10% of the class regardless of the score), are you better off with a grade of 81 on this exam or a grade of 68 on a different exam where the mean is 62 and the standard deviation is 3? show statistically and explain<BR>\n" );
document.write( "Include a normal distribution curve<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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