document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132731>Question 1132731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! <BR>\n" );
document.write( "Can you help explain this problem?<BR>\n" );
document.write( "The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews.  From past records, they have found that the length of a first interview is normally distributed with mean u=35 minutes and standard deviation q=7 minutes.<BR>\n" );
document.write( "a) WHat is the probability that the interview will last 40 minutes or longer?<BR>\n" );
document.write( "b)Nine first interviews are usually scheduled per day. What is the probability that the average length of time for the 9 interviews will be 40 minutes or longer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749878 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=749878\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the mean is 35 minutes with a standard deviation of 7 minutes.\r<BR>\n" );
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document.write( "you need to find the z-score.\r<BR>\n" );
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document.write( "the formula for z-score is z = (x - m) / s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw score mean<BR>\n" );
document.write( "s is the standard deviation of the popluation.\r<BR>\n" );
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document.write( "z = (40 - 35) / 7 = .7142857143 through use of my TI-84 Plus calculator.\r<BR>\n" );
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document.write( "the probability of getting a z-score greater than that is equal to .2375251875 through use of my TI-84 Plus calculator.\r<BR>\n" );
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document.write( "that is not normally considered unusual.\r<BR>\n" );
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document.write( "a probability of less than .05 would normally be considered unusual, but it really depends on what you would consider unusual when you make the statistical test.\r<BR>\n" );
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document.write( "that can vary based on the requirements of the test.\r<BR>\n" );
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document.write( ".05 is normally considered, but other tests have different requirements, such as less than .025 or less than .01 or less than .10.\r<BR>\n" );
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document.write( "you would have to decide before you make the test what you would consider unusual and then you would make the test and determine if the results are to be considered unusual or not based on the results of that test.\r<BR>\n" );
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document.write( "when you take a sample of 9 people and look at the mean of that sample, the standard deviation of the sample means is different from the standard deviation of an individual score used above.\r<BR>\n" );
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document.write( "the formula for the standard deviation of the distribution of sample means (called the standard error) is calculated as follows:\r<BR>\n" );
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document.write( "s = standard deviation of the population divided by the square root of the sample size.\r<BR>\n" );
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document.write( "in this case, s would be equal to 7 / sqrt(9) = 2.3333333.....\r<BR>\n" );
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document.write( "the standard deviation of the distribution of sample means will get smaller as the size of the sample gets larger.\r<BR>\n" );
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document.write( "your z-score, in this case, becomes z = (40 - 35) / 2.33333..... = 2.142857143.\r<BR>\n" );
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document.write( "the probability of getting a z-score greater than 2.142857143 is equal to .0160622279 through the use of my TI-84 Plus calculator.\r<BR>\n" );
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document.write( "that would be considered unusual in most tests since it is a very small probability.\r<BR>\n" );
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document.write( "you are not talking about an individual score any more.\r<BR>\n" );
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document.write( "you are talking about the mean of a number of scores in the sample.\r<BR>\n" );
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document.write( "you do not expect the mean of a number of scores in a sample to vary as much from the mean of the population, and the larger the sample, the less you expect the mean of that sample to vary from the population mean.\r<BR>\n" );
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document.write( "the variance from the mean of a number of scores will get smaller as the number of scores in the sample gets larger.\r<BR>\n" );
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document.write( "note that standard deviation is the square root of the variance, so they're very closely related.\r<BR>\n" );
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document.write( "when the size of the sample gets as large as the population itself, than the variance in the distribution of sample means becomes 0 because the mean of each sample is the mean of the population and will therefore not vary from it.\r<BR>\n" );
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document.write( "visually, the distribution of your sample means from a sample of 1 looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011501.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "and the distribution of your sample means from a sample of 9 looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/011502.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "note that when you are taking an individual score from the population, your sample size is 1 and the mean of the sample is the sample score itself and your standard error is the standard deviation of the population itself.\r<BR>\n" );
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document.write( "consider the formula for standard error = standard deviation of the population divided by square root of sample size.\r<BR>\n" );
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document.write( "standard error, in this case = 7 / sqrt(1) = 7.\r<BR>\n" );
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