document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328285>Question 328285</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A painter has learned that the time it takes her to paint a random room in a house is normally distributed with a mean if 4 hours and a standard deviation of 45 minutes. If she is just starting work on a random room and has to leave in five hour, find<BR>\n" );
document.write( "a. The probablilty  she can have lunch before she has to leave if she needs 30min. for lunch.<BR>\n" );
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document.write( "b. the probability she does not finish before she leaves.\r<BR>\n" );
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document.write( "c. The probability she works for more that 3 hours (don't forget she will stop working to leave on time.)\r<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 #235203 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=235203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A painter has learned that the time it takes her to paint a random room in a house is normally distributed with a mean of 4 hours and a standard deviation of 45 minutes.<BR>\n" );
document.write( "If she is just starting work on a random room and has to leave in five hour, find<BR>\n" );
document.write( "a. The probablilty she can have lunch before she has to leave if she needs 30min. for lunch.<BR>\n" );
document.write( "She will be home for 4 1/2 hrs<BR>\n" );
document.write( "P(the job and lunch will be <= 4.5 hrs) = ?<BR>\n" );
document.write( "z(4.5) = (4.5-4)/0.75 = 2.3<BR>\n" );
document.write( "So, P(she can do job and lunch) = P(z< 2/3) = 0.7475<BR>\n" );
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document.write( "b. the probability she does not finish before she leaves.<BR>\n" );
document.write( "P(x > 5) = ?<BR>\n" );
document.write( "z(5) = (5-4)/0.75 = 4/3<BR>\n" );
document.write( "So, P(x > 5) = P(z > 4/3) = 0.0912<BR>\n" );
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document.write( "c. The probability she works for more that 3 hours (don't forget she will stop working to leave on time.)<BR>\n" );
document.write( "P(3< x < 5) = ?<BR>\n" );
document.write( "z(3) = (3-4)/0.75 = -4/3<BR>\n" );
document.write( "So, P(3 < x < 5) = P(-4/3 < z < 4/3) = 0.8176<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  <BR>\n" );
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