document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1002065>Question 1002065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear tutor,\r<BR>\n" );
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document.write( "I am having a problem with standard normal distribution table. I have been reading difference between positive and negative z values. but I am still having a hard time. For example, please see the question below.\r<BR>\n" );
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document.write( "Q.Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.<BR>\n" );
document.write( "On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.\r<BR>\n" );
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document.write( "a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.<BR>\n" );
document.write( "I used calculator normalcdf (30, 10^99, 28, 5) = 0.3446<BR>\n" );
document.write( "but the book calculated z score first 30-28/5 = 0.4 <-- I got this part!<BR>\n" );
document.write( "From the normal table (this part is confusing)<BR>\n" );
document.write( "Area to the right of 0.4 = 1- (0.5 + 0.15542) = 0.3446 <---- Not sure where this formula came from.If it is 0.4 why is not 0.6554 like on the table?\r<BR>\n" );
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document.write( "The required probability is 0.3446.<BR>\n" );
document.write( "Answer is the same but trying to figure it out how to do it without using calculator....\r<BR>\n" );
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document.write( "b.Find the 95th percentile, and express it in a sentence.<BR>\n" );
document.write( "InvNorm (0.95, 28, 5) = 36.2243<BR>\n" );
document.write( "As explained in the book :<BR>\n" );
document.write( "Area to the left = 0.95<BR>\n" );
document.write( "From the normal table we need to find the area value closest to 0.95 - 0.5 = 0.45 and get the corresponding z-score. The closest match lower than 0.45 that we can get on the table is 0.44950 and the corresponding z-score value is 1.64.<BR>\n" );
document.write( "- I do not understand this part at all.....what can't we just look at the table for 0.95? <BR>\n" );
document.write( "Now we convert the z-score 1.64 to the x value using the formula (understand this formula)<BR>\n" );
document.write( "z * sd = x - mean<BR>\n" );
document.write( "x = z * sd + mean = 1.64 *5 + 28 = 36.2\r<BR>\n" );
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document.write( "thank you in advance!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #619079 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=619079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Dear tutor,<BR>\n" );
document.write( "Q.Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.<BR>\n" );
document.write( "On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.\r<BR>\n" );
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document.write( "i believe you will find that the book may be giving you the half table rather than the full table.\r<BR>\n" );
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document.write( "there are 2 different types of tables most commonly used.\r<BR>\n" );
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document.write( "the full table shows you z-scores from - 3.5 or so to + 3.5 or so.\r<BR>\n" );
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document.write( "you read .95 directly from this table.\r<BR>\n" );
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document.write( "the half table shows you z-scores from 0 to + 3.5 or so.\r<BR>\n" );
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document.write( "this table is only showing you the right half of the distribution curve.\r<BR>\n" );
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document.write( "i have both tables and can show you how to do it from each.\r<BR>\n" );
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document.write( "a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.\r<BR>\n" );
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document.write( "m = mean<BR>\n" );
document.write( "x = raw score<BR>\n" );
document.write( "s = standard deviation\r<BR>\n" );
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document.write( "z = (x-m)/s\r<BR>\n" );
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document.write( "x = 30<BR>\n" );
document.write( "m = 28<BR>\n" );
document.write( "s = 5\r<BR>\n" );
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document.write( "z = (30-28)/5 = 2/5 = .4\r<BR>\n" );
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document.write( "using the full table:\r<BR>\n" );
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document.write( "look up a z-score of .4 and it will tell you that the area to the left of that z-score is .6554.\r<BR>\n" );
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document.write( "you want the area to the right of the z-score, so you take 1 - .6554 to get .3446.\r<BR>\n" );
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document.write( "using the half table:\r<BR>\n" );
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document.write( "look up the z-score of .4 and it will tell you that the area to the left of that z-score is .1554.\r<BR>\n" );
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document.write( "you want the area to the right of that z-score.\r<BR>\n" );
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document.write( ".5 - .1554 = .3446\r<BR>\n" );
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document.write( "same answer only you got it a different way.\r<BR>\n" );
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document.write( "-----\r<BR>\n" );
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document.write( "b.Find the 95th percentile, and express it in a sentence.\r<BR>\n" );
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document.write( "using the full table:\r<BR>\n" );
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document.write( "look up the area to the left of the z-score that is closest to .95\r<BR>\n" );
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document.write( "you will find .9495 and .9505\r<BR>\n" );
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document.write( ".9495 is a z-score of 1.64<BR>\n" );
document.write( ".9505 is a z-score of 1.65\r<BR>\n" );
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document.write( "split the difference and you get a z-score of 1.645.\r<BR>\n" );
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document.write( "using the half table:\r<BR>\n" );
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document.write( "look up an area to the left of the z-score that is closest to  .95 - .5 = .45\r<BR>\n" );
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document.write( "you have to subtract .5 because the area to the left of the z-score in the half table is only to the midpoint of the distribution curve because it is dealing only with the right side of the distribution curve.\r<BR>\n" );
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document.write( "the half table will tell you that the areas closest to .45 are .4495 and .4505.<BR>\n" );
document.write( "those areas correspond to z-scores of 1.64 and 1.65.<BR>\n" );
document.write( "split the difference and you get a z-score of 1.645.\r<BR>\n" );
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document.write( "same result as the full table only you got it a different way.\r<BR>\n" );
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document.write( "-----\r<BR>\n" );
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document.write( "your calculator assumes full table.\r<BR>\n" );
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document.write( "if you have to use the table, use the full table rather than the half table.\r<BR>\n" );
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document.write( "you can experiment with the half table and get your answer using that as well as the full table as well as the calculator.\r<BR>\n" );
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document.write( "the answers should be the same if you round to the same number of decimal places.\r<BR>\n" );
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document.write( "here's an example of the use of the half table compared to the full table.\r<BR>\n" );
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document.write( "how do you find the area to the left of -1.5?\r<BR>\n" );
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document.write( "with the full table, you look up -1.5 and it will tell you that the area to the left is equal to .0668\r<BR>\n" );
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document.write( "with the half table, you look up 1.5 and it will tell you that the area to the left is equal to .4332.\r<BR>\n" );
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document.write( "since the right half of the table is the mirror image of the left half of the table, you do not want the area to the left.<BR>\n" );
document.write( "you want the area to the right.<BR>\n" );
document.write( "using the half table, that would be .5 - .4332 = .0668\r<BR>\n" );
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document.write( "the area to the right of 1.5 is the same as the area to the left of -1.5<BR>\n" );
document.write( "that's because the table is symmetric about the mean and the mean is always in the center of the normal distribution.\r<BR>\n" );
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document.write( "one more examle for good measure.\r<BR>\n" );
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document.write( "find the area between a z-score of -1 and 1.\r<BR>\n" );
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document.write( "using the full table:\r<BR>\n" );
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document.write( "find area to the left of 1 and area to the left of -1 and then subtract the smaller area from the larger area.\r<BR>\n" );
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document.write( "area to the left of z-score of 1 is .8413<BR>\n" );
document.write( "area to the left of z-score of -1 is .1587<BR>\n" );
document.write( "area between -1 and 1 is .8413 - .1587 = .6826\r<BR>\n" );
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document.write( "using the half table:\r<BR>\n" );
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document.write( "find area to the left of 1.<BR>\n" );
document.write( "you will get area to the left of 1 is .3413<BR>\n" );
document.write( "double that to get .6826\r<BR>\n" );
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document.write( "why double it?\r<BR>\n" );
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document.write( "left side is mirror image of right side.<BR>\n" );
document.write( "area to the left of 1 is .3413<BR>\n" );
document.write( "in the mirror image, this is the same as area to the right of -1.<BR>\n" );
document.write( "area to the right of -1 is .3413<BR>\n" );
document.write( "area between -1 and 1 is .6826.\r<BR>\n" );
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document.write( "you have to play with it for a while to become comfortable with it.<BR>\n" );
document.write( "most times you will probably use a calculator.<BR>\n" );
document.write( "most other times you will probably use a full table.<BR>\n" );
document.write( "you would not normally use a half table unless that's all that is available.\r<BR>\n" );
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document.write( "here's some links to the tables i used plus a link to an online calculator you might find very interesting and useful.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf\" target = \"_blank\">FULL TABLE</><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.intmath.com/counting-probability/z-table.php\" target = \"_blank\">HALF TABLE</><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">CALCULATOR</>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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