document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207169>Question 1207169</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P17, the 17-percentile. This is the temperature reading separating the bottom 17% from the top 83%.\r<BR>\n" );
document.write( "\n" );
document.write( "P17 = <BR>\n" );
document.write( "°C<BR>\n" );
document.write( "distribution of values is normal with a mean of 167.9 and a standard deviation of 82.\r<BR>\n" );
document.write( "\n" );
document.write( "Find P84, which is the score separating the bottom 84% from the top 16%.<BR>\n" );
document.write( "P84 = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.<BR>\n" );
document.write( "Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.4-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 0.5% or largest 0.5%.\r<BR>\n" );
document.write( "\n" );
document.write( "What is the minimum head breadth that will fit the clientele?<BR>\n" );
document.write( "min = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "What is the maximum head breadth that will fit the clientele?<BR>\n" );
document.write( "max = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.<BR>\n" );
document.write( "Here is the full question:\r<BR>\n" );
document.write( "\n" );
document.write( "Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9926, find d.\r<BR>\n" );
document.write( "\n" );
document.write( "d =\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 #844891 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P17, the 17-percentile. This is the temperature reading separating the bottom 17% from the top 83%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you are looking for a z-score that have .17 area to the left of it and .83 area to the right of it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the z-score that has area of .17 to the left of it is equal to -.954.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that same z-score will have an area to the right of it of .83.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "herre are the results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042812.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042813.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "distribution of values is normal with a mean of 167.9 and a standard deviation of 82.<BR>\n" );
document.write( "Find P84, which is the score separating the bottom 84% from the top 16%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score formula results are shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042814.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042815.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to find the raw score, use the z-score formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when the mean is 167.9 and the standard deviation is 82, the raw score associated with a z-score of .994 is calculated as follows:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (x-m)/s becomes .994 = (x-167.9) / 82.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = .994 * 82 + 167.9 = 249.498.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of getting a raw score less than that is .84 and the probability of getting a raw score greater than that is .16.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.4-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 0.5% or largest 0.5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your confidence interval is .99.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that leave .005 area to the left of the confidence interval and .005 area to the right of the confidence interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".005 is equivalent to .5%.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".5% on the left and right of the confidence total 1% which is equal to .01.<BR>\n" );
document.write( "the confidence interval is therefore equal to 99% of the area under the normal distribution curve, which is equal to .99.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the critical z-scores at .99 confidence interval are plus or minus 2.576 as shown in the following calculator results.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042816.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the raw scores are found using the z-score formula as shown below.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "when z = plus or minus 2.576 and mean = 6.4 and standard deviation = .8, you get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "minimum z-score = -2.576 = (x - 6.4) / .8.<BR>\n" );
document.write( "solve for x to get x = -2.576 * .8 + 6.4 = 4.3392.<BR>\n" );
document.write( "that's the minimum head breadth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "maximum z-score = 2.576 = (x - 6.4) / .8.<BR>\n" );
document.write( "solve for x to get x = 2.576 * .8 + 6.4 = 8.4608.<BR>\n" );
document.write( "that's the maximum head breadth.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's what it looks like on a z-score calculator.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/042817.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.<BR>\n" );
document.write( "Here is the full question:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9926, find d.<BR>\n" );
document.write( "d = \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this was answered previously.<BR>\n" );
document.write( "the answer was d = -2.437.<BR>\n" );
document.write( "that's the z-score that has .9926 of the area under the normal distribution curve to the right of it.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );