document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169482>Question 1169482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving the following (not sure what steps I have to take to get the correct answer)\r<BR>\n" );
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document.write( "Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 238 feet and a standard deviation of 58 feet. We randomly sample 49 fly balls. \r<BR>\n" );
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document.write( "1. If X= average distance in feet for 49 fly balls, then what's the distribution of X? (Must round your standard deviation to two decimal places)\r<BR>\n" );
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document.write( "2. What is the probability that the 49 balls traveled an average of less than 226 feet? (Round your answer to four decimal places.)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794327 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=794327\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mean = 238<BR>\n" );
document.write( "standard deviation = 58<BR>\n" );
document.write( "sample size = 49\r<BR>\n" );
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document.write( "standard error = standard deviation / square root of sample size.\r<BR>\n" );
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document.write( "standard error = 58/sqrt(49) = 58/7 = 8.285714286.\r<BR>\n" );
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document.write( "z-score = (x - m) / s\r<BR>\n" );
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document.write( "x is the raw score<BR>\n" );
document.write( "m ie the mean<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
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document.write( "z-score = (226 - 238) / 8.285714286 = -1.448275862\r<BR>\n" );
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document.write( "this can be rounded to -1.45 if you use the z-score tables.\r<BR>\n" );
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document.write( "it can be left as is if you use a calculator that can handle it.\r<BR>\n" );
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document.write( "i use the ti-84 plus which can handle it.\r<BR>\n" );
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document.write( "using the ti-84 plus, i get an area to the left of a z-score of -1.448275862 equal to .073769999.\r<BR>\n" );
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document.write( "that's the probability that the average of fly balls in the sample will be less than 226.\r<BR>\n" );
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document.write( "if use the z-score table, then the area to the left of a z-score of -1.45 is equal to .07353.\r<BR>\n" );
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document.write( "both results are acceptable.\r<BR>\n" );
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document.write( "the difference between .07353 and .073769999 is approximately 0.325% of .073769999.\r<BR>\n" );
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document.write( "that's well within the accuracy required.\r<BR>\n" );
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document.write( "here's what the result looks like using the online calculator that can be found at <a  rel=nofollow HREF= \"https://www.calculator.net/z-score-calculator.html?c1raw=226&c1mean=238&c1sd=8.285714286&calctype=zscore&x=60&y=17\" target = \"_blank\">https://www.calculator.net/z-score-calculator.html?c1raw=226&c1mean=238&c1sd=8.285714286&calctype=zscore&x=60&y=17</a>\r<BR>\n" );
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