document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204718>Question 204718</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inches. What is the probability that a randomly selected Ping-Pong ball will have a diameter of: <BR>\n" );
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document.write( "a. Between 1.28 and 1.30 inches?<BR>\n" );
document.write( "b. Between 1.31 and 1.33 inches?<BR>\n" );
document.write( "c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)?\r<BR>\n" );
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document.write( "   If random samples of 16 Ping-Pong balls were selected, <BR>\n" );
document.write( "d. What proportion of the sample means would be between 1.31 and 1.33 inches? \r<BR>\n" );
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document.write( "   If random samples of 100 Ping-Pong balls were selected, <BR>\n" );
document.write( "e. What proportion of the sample means would be between 1.31 and 1.33 inches?<BR>\n" );
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document.write( "f. Compare your results in (b), (d) and (e). <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 #154586 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=154586\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diameter of Ping-Pong balls manufactured at a large factory is expected to be approximately normally distributed with a mean of 1.30 inches and a standard deviation of 0.04 inches.<BR>\n" );
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document.write( "If you don't have software or a calculator you will have to do these using<BR>\n" );
document.write( "z-values and a z-chart.  My answers are based on using a TI calculator.<BR>\n" );
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document.write( " What is the probability that a randomly selected Ping-Pong ball will have a diameter of: \r<BR>\n" );
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document.write( "a. Between 1.28 and 1.30 inches?<BR>\n" );
document.write( "Ans: normalcdf(1.28,1.30,1.30,0.04) = 0.1915<BR>\n" );
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document.write( "b. Between 1.31 and 1.33 inches?<BR>\n" );
document.write( "Ans: normalcdf(1.31,1.33,1.30,0.04) = 0.1747<BR>\n" );
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document.write( "c. Between what two values will 60% of the Ping-Pong balls fall (in terms of the diameter)? <BR>\n" );
document.write( "You need the z-value that is 30% to the right and 30% to the left of the<BR>\n" );
document.write( "mean.  That value is InvNorm(0.20) = 0.8416<BR>\n" );
document.write( "Then you have to use x = u + z*sugma to find the correct x-values<BR>\n" );
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document.write( "If random samples of 16 Ping-Pong balls were selected, <BR>\n" );
document.write( "d. What proportion of the sample means would be between 1.31 and 1.33 inches? <BR>\n" );
document.write( "If random samples of 100 Ping-Pong balls were selected,<BR>\n" );
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document.write( "The standard deviation has changed to 0.04/sqrt(16) = 0.01 because of <BR>\n" );
document.write( "the Central Limit Theorem.<BR>\n" );
document.write( "Ans: normalcdf(1.31,1.33,1.3,0.01) = 0.1573<BR>\n" );
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document.write( "I'll leave the rest to you.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "e. What proportion of the sample means would be between 1.31 and 1.33 inches?\r<BR>\n" );
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document.write( "f. Compare your results in (b), (d) and (e). <BR>\n" );
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