document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251866>Question 251866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help with word problems, thank you!\r<BR>\n" );
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document.write( "The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. (a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg of caffeine? (b) Less than 100 mg? (c) A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will have less caffeine than a very strong cup of tea? (Data are from Popular Science 254, no. 5 [May 1999], p. 95.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183599 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=183599\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg with a standard deviation of 20 mg. <BR>\n" );
document.write( "(a) What is the probability that a randomly chosen cup of home-brewed coffee will have more than 130 mg of caffeine? <BR>\n" );
document.write( "Find the z-value of 130<BR>\n" );
document.write( "Then P(x > 130) = P(z > that z-value)<BR>\n" );
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document.write( "(b) Less than 100 mg?<BR>\n" );
document.write( "Find the z-value of 100.<BR>\n" );
document.write( "Then P(x<100) = P(z< that z-value)<BR>\n" );
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document.write( "(c) A very strong cup of tea has a caffeine content of 91 mg. What is the probability that a cup of coffee will have less caffeine than a very strong cup of tea?<BR>\n" );
document.write( "Find the z-value that corresponds to 91 mg using<BR>\n" );
document.write( "x = z*sigma + u<BR>\n" );
document.write( "91 = z*20+115<BR>\n" );
document.write( "z = -1.2<BR>\n" );
document.write( "-<BR>\n" );
document.write( "Find P(z < -1.2)<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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