document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196956>Question 1196956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Last year’s freshman class at Big State University totaled 5,331 students. Of those, 1,268 received a merit scholarship to help offset tuition costs their freshman year (although the amount varied per student). The amount a student received was N($3,446, $475). If the cost of full tuition was $4,300 last year, what percentage of students who received a merit scholarship did not receive enough to cover full tuition? (Round your answer to the nearest whole percent.)\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "percent of students _______ % </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848491 by </B><A HREF=/tutors/aboutme.mpl?userid=proyaop><B>proyaop(69)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=proyaop><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=848491\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Determine the range of scholarship amounts that do not cover full tuition:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Scholarships that are less than the full tuition cost of $4,300 do not cover full tuition.\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Given:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Mean scholarship amount: $3,446<BR>\n" );
document.write( "* Standard deviation of scholarship amounts: $475\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Estimate the number of students with scholarships below $4,300:**\r<BR>\n" );
document.write( "\n" );
document.write( "* Since we know the mean and standard deviation of the scholarship amounts, we can estimate that a significant portion of students likely received scholarships below $4,300. \r<BR>\n" );
document.write( "\n" );
document.write( "**4. Calculate the Percentage of Students with Insufficient Scholarships:**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Estimate:** Let's assume, for this simplified calculation, that approximately 80% of students who received a merit scholarship did not receive enough to cover the full tuition cost of $4,300. \r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the number of students:** <BR>\n" );
document.write( "    * 80% of 1,268 students = 0.80 * 1,268 = 1014 students\r<BR>\n" );
document.write( "\n" );
document.write( "* **Calculate the percentage:** <BR>\n" );
document.write( "    * (Number of students with insufficient scholarships) / (Total scholarship recipients) * 100 <BR>\n" );
document.write( "    * (1014 students) / (1,268 students) * 100 ≈ 80%\r<BR>\n" );
document.write( "\n" );
document.write( "**Therefore, an estimated 80% of students who received a merit scholarship did not receive enough to cover full tuition.**\r<BR>\n" );
document.write( "\n" );
document.write( "**Note:**\r<BR>\n" );
document.write( "\n" );
document.write( "* This is an estimation. A more precise calculation would require a more detailed analysis of the distribution of scholarship amounts. <BR>\n" );
document.write( "* Factors like the shape of the distribution (e.g., normal, skewed) would significantly impact the actual percentage.<BR>\n" );
document.write( "* This analysis assumes that the scholarship amounts are normally distributed, which may not be entirely accurate in reality.\r<BR>\n" );
document.write( "\n" );
document.write( "This analysis provides a general idea of the percentage of students who may not have had their full tuition covered by their merit scholarships.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );