document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178715>Question 1178715</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve each problem.<BR>\n" );
document.write( "1. Your monthly electric bill has a mean of ₱120.00. what is the percentage that you will pay an amount between ₱1,380 and ₱1,740?\r<BR>\n" );
document.write( "\n" );
document.write( "2.Suppose the scores in the mathematics exam are normally distributed. If the exam has a mean score of 25 and a standard deviation of 5,what is the probability that if you take the exam you will get a score higher than 30 points? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850305 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850305\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve each problem step-by-step:\r<BR>\n" );
document.write( "\n" );
document.write( "**Problem 1: Monthly Electric Bill**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Understanding the Issue:**<BR>\n" );
document.write( "    * The mean monthly electric bill is given as ₱120.00.<BR>\n" );
document.write( "    * The amounts ₱1,380 and ₱1,740 are extremely far from the mean, suggesting there might be an error in the problem statement. It's highly unlikely that monthly bills would be in those amounts.<BR>\n" );
document.write( "    * To solve this problem, we need a standard deviation. Let's assume a standard deviation of ₱15.00.<BR>\n" );
document.write( "* **Calculations:**<BR>\n" );
document.write( "    1.  **Calculate z-scores:**<BR>\n" );
document.write( "        * z1 = (1380 - 120) / 15 = 1260 / 15 = 84<BR>\n" );
document.write( "        * z2 = (1740 - 120) / 15 = 1620 / 15 = 108<BR>\n" );
document.write( "    2.  **Find probabilities:**<BR>\n" );
document.write( "        * Because the z-scores are so high, the probability of the bill being in that range is extremely close to 0.<BR>\n" );
document.write( "* **Answer:**<BR>\n" );
document.write( "    * The probability is essentially 0.\r<BR>\n" );
document.write( "\n" );
document.write( "**Problem 2: Mathematics Exam Scores**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Understanding the Issue:**<BR>\n" );
document.write( "    * The exam scores are normally distributed.<BR>\n" );
document.write( "    * Mean score (μ) = 25<BR>\n" );
document.write( "    * Standard deviation (σ) = 5<BR>\n" );
document.write( "    * We want to find the probability of scoring higher than 30.<BR>\n" );
document.write( "* **Calculations:**<BR>\n" );
document.write( "    1.  **Calculate the z-score:**<BR>\n" );
document.write( "        * z = (X - μ) / σ = (30 - 25) / 5 = 5 / 5 = 1<BR>\n" );
document.write( "    2.  **Find the probability:**<BR>\n" );
document.write( "        * P(X > 30) = P(z > 1)<BR>\n" );
document.write( "        * Using a z-table or calculator:<BR>\n" );
document.write( "            * P(z < 1) ≈ 0.8413<BR>\n" );
document.write( "            * P(z > 1) = 1 - P(z < 1) ≈ 1 - 0.8413 = 0.1587<BR>\n" );
document.write( "* **Answer:**<BR>\n" );
document.write( "    * The probability of scoring higher than 30 is approximately 0.1587, or 15.87%.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );