document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190589>Question 1190589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Greetings, \r<BR>\n" );
document.write( "\n" );
document.write( "I solved part of this problem, just need a bit of help with the second part. Thank you, I greatly appreciate it!\r<BR>\n" );
document.write( "\n" );
document.write( "When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X	1	2	3	4	5	6	7	8<BR>\n" );
document.write( "P(X)	0.2	0.119	0.128	0.079	0.058	0.03	0.036	0.35\r<BR>\n" );
document.write( "\n" );
document.write( "(I solved these 2 answers)<BR>\n" );
document.write( "A. Mean = 4.66<BR>\n" );
document.write( "B. Standard Dev. = 2.8408\r<BR>\n" );
document.write( "\n" );
document.write( "The cost of parking is 2.75 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates.\r<BR>\n" );
document.write( "\n" );
document.write( "(I solved this)<BR>\n" );
document.write( "A. Mean = 12.815\r<BR>\n" );
document.write( "\n" );
document.write( "B. Standard Deviation = ????\r<BR>\n" );
document.write( "\n" );
document.write( "I can't seem to figure of the standard deviation.\r<BR>\n" );
document.write( "\n" );
document.write( "I appreciate your help. \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822291 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=822291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Question 1, part A\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Given data table<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >P(X)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Form a new row consisting of X*P(X)<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >P(X)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr><tr><TD >X*P(X)</TD><TD >0.2</TD><TD >0.238</TD><TD >0.384</TD><TD >0.316</TD><TD >0.29</TD><TD >0.18</TD><TD >0.252</TD><TD >2.8</TD></tr>\n" );
document.write( "</TABLE>For example, 8*0.35 = 2.8 in the far right column.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add up everything in the X*P(X) row<BR>\n" );
document.write( "0.2+0.238+0.384+0.316+0.29+0.18+0.252+2.8 = 4.66\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Your answer of 4.66 is perfectly correct. Nice work.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question 1, part B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Form a new row that involves subtracting each X value from the mean mu = 4.66<BR>\n" );
document.write( "Afterward, square the result<BR>\n" );
document.write( "The expression is of the form (X-mu)^2 which is what I'll title this new row.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >P(X)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr><tr><TD >X*P(X)</TD><TD >0.2</TD><TD >0.238</TD><TD >0.384</TD><TD >0.316</TD><TD >0.29</TD><TD >0.18</TD><TD >0.252</TD><TD >2.8</TD></tr><tr><TD >(X-mu)^2</TD><TD >13.3956</TD><TD >7.0756</TD><TD >2.7556</TD><TD >0.4356</TD><TD >0.1156</TD><TD >1.7956</TD><TD >5.4756</TD><TD >11.1556</TD></tr>\n" );
document.write( "</TABLE>Example: In column 1 we have<BR>\n" );
document.write( "(X-mu)^2 = (1-4.66)^2 = 13.3956\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, multiply each (X-mu)^2 value with its corresponding P(X) value. <BR>\n" );
document.write( "I'll make a new row for that.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >P(X)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr><tr><TD >X*P(X)</TD><TD >0.2</TD><TD >0.238</TD><TD >0.384</TD><TD >0.316</TD><TD >0.29</TD><TD >0.18</TD><TD >0.252</TD><TD >2.8</TD></tr><tr><TD >(X-mu)^2</TD><TD >13.3956</TD><TD >7.0756</TD><TD >2.7556</TD><TD >0.4356</TD><TD >0.1156</TD><TD >1.7956</TD><TD >5.4756</TD><TD >11.1556</TD></tr><tr><TD >(X-mu)^2*P(X)</TD><TD >2.67912</TD><TD >0.8419964</TD><TD >0.3527168</TD><TD >0.0344124</TD><TD >0.0067048</TD><TD >0.053868</TD><TD >0.1971216</TD><TD >3.90446</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then add up everything in the (X-mu)^2*P(X) row<BR>\n" );
document.write( "2.67912+0.8419964+0.3527168+0.0344124+0.0067048+0.053868+0.1971216+3.90446 = 8.0704\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The last step is to apply the square root<BR>\n" );
document.write( "sqrt(8.0704) = 2.8408\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The standard deviation is approximately 2.8408\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You're on a roll with correct answers.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question 2, part A\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "X = number of hours parked<BR>\n" );
document.write( "Y = revenue<BR>\n" );
document.write( "To find the revenue, we multiply 2.75 by the X value<BR>\n" );
document.write( "Y = 2.75X\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For example, if a car is parked for 4 hours, then<BR>\n" );
document.write( "Y = 2.75*X = 2.75*4 = 11<BR>\n" );
document.write( "meaning they pull in $11 in revenue\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's form a table of Y values with their corresponding P(Y) probabilities.<BR>\n" );
document.write( "The probabilities will be the same as before. The only thing that changes is the introduction of the Y row.<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >Y</TD><TD >2.75</TD><TD >5.5</TD><TD >8.25</TD><TD >11</TD><TD >13.75</TD><TD >16.5</TD><TD >19.25</TD><TD >22</TD></tr><tr><TD >P(Y)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr>\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We follow the same steps as part A in the previous question. I'll skip a few steps, but basically this is what you should have as a final table<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >Y</TD><TD >2.75</TD><TD >5.5</TD><TD >8.25</TD><TD >11</TD><TD >13.75</TD><TD >16.5</TD><TD >19.25</TD><TD >22</TD></tr><tr><TD >P(Y)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr><tr><TD >Y*P(Y)</TD><TD >0.55</TD><TD >0.6545</TD><TD >1.056</TD><TD >0.869</TD><TD >0.7975</TD><TD >0.495</TD><TD >0.693</TD><TD >7.7</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Adding everything in that bottom row gets you 12.815\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You have the correct answer once again.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "================================================\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Question 2, part B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We follow the same steps as part B from the previous question<BR>\n" );
document.write( "This time use mu = 12.815 which was found in the previous section.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is what the table should look like when all is said and done<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >X</TD><TD >1</TD><TD >2</TD><TD >3</TD><TD >4</TD><TD >5</TD><TD >6</TD><TD >7</TD><TD >8</TD></tr><tr><TD >Y</TD><TD >2.75</TD><TD >5.5</TD><TD >8.25</TD><TD >11</TD><TD >13.75</TD><TD >16.5</TD><TD >19.25</TD><TD >22</TD></tr><tr><TD >P(Y)</TD><TD >0.2</TD><TD >0.119</TD><TD >0.128</TD><TD >0.079</TD><TD >0.058</TD><TD >0.03</TD><TD >0.036</TD><TD >0.35</TD></tr><tr><TD >Y*P(Y)</TD><TD >0.55</TD><TD >0.6545</TD><TD >1.056</TD><TD >0.869</TD><TD >0.7975</TD><TD >0.495</TD><TD >0.693</TD><TD >7.7</TD></tr><tr><TD >(Y-mu)^2</TD><TD >101.304225</TD><TD >53.509225</TD><TD >20.839225</TD><TD >3.294225</TD><TD >0.874225</TD><TD >13.579225</TD><TD >41.409225</TD><TD >84.364225</TD></tr><tr><TD >(Y-mu)^2*P(Y)</TD><TD >20.260845</TD><TD >6.367597775</TD><TD >2.6674208</TD><TD >0.260243775</TD><TD >0.05070505</TD><TD >0.40737675</TD><TD >1.4907321</TD><TD >29.52747875</TD></tr>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "Add up everything in the bottom row and you should get 61.0324\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Apply the square root to get<BR>\n" );
document.write( "sqrt(61.0324) = 7.8123<BR>\n" );
document.write( "The value is approximate.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This is a useful calculator to check your work<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php\">https://www.mathportal.org/calculators/statistics-calculator/probability-distributions-calculator.php</a><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );