document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180480>Question 1180480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A.Three hundred thirthy five students participated in a field demonstration.Their heights averaged 105 cm with a standard deviation of 5cm.<BR>\n" );
document.write( "1.What is the probability that a student picked at random has a height greater than 116cm?<BR>\n" );
document.write( "2.What is the probability that height of a student picked at random is less than 104cm? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850109 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to solve this problem:\r<BR>\n" );
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document.write( "**1. Calculate the z-scores:**\r<BR>\n" );
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document.write( "A z-score tells you how many standard deviations a particular value is from the mean.  The formula is:\r<BR>\n" );
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document.write( "z = (x - μ) / σ\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "*   x = the value you're interested in<BR>\n" );
document.write( "*   μ = the mean<BR>\n" );
document.write( "*   σ = the standard deviation\r<BR>\n" );
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document.write( "*   **For x = 116 cm:**<BR>\n" );
document.write( "    z = (116 - 105) / 5<BR>\n" );
document.write( "    z = 11 / 5<BR>\n" );
document.write( "    z = 2.2\r<BR>\n" );
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document.write( "*   **For x = 104 cm:**<BR>\n" );
document.write( "    z = (104 - 105) / 5<BR>\n" );
document.write( "    z = -1 / 5<BR>\n" );
document.write( "    z = -0.2\r<BR>\n" );
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document.write( "**2. Find the probabilities using a z-table or calculator:**\r<BR>\n" );
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document.write( "A z-table (or a calculator with statistical functions) gives you the probability of a value being *less than* a given z-score.\r<BR>\n" );
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document.write( "*   **P(height > 116 cm):**  We want the probability of a height *greater* than 116 cm, so we need to find the area to the *right* of z = 2.2.<BR>\n" );
document.write( "    P(z > 2.2) = 1 - P(z < 2.2)<BR>\n" );
document.write( "    Look up P(z < 2.2) in the z-table. It's approximately 0.9861.<BR>\n" );
document.write( "    P(z > 2.2) = 1 - 0.9861 = 0.0139\r<BR>\n" );
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document.write( "*   **P(height < 104 cm):** We want the probability of a height *less* than 104 cm, so we need the area to the *left* of z = -0.2.<BR>\n" );
document.write( "    P(z < -0.2)<BR>\n" );
document.write( "    Look up P(z < -0.2) in the z-table. It's approximately 0.4207.\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "1.  The probability that a randomly picked student has a height greater than 116 cm is approximately 0.0139 or 1.39%.\r<BR>\n" );
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document.write( "2.  The probability that a randomly picked student has a height less than 104 cm is approximately 0.4207 or 42.07%.<BR>\n" );
document.write( " </SPAN>\n" );
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