document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123913>Question 123913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am new to Statisitics and having problem understanding this question.  Kindly help me.\r<BR>\n" );
document.write( "\n" );
document.write( "In a certain microwave oven on the high power setting, the time it takes a randomly chosden kernel of popcorn to pop is normally distributed with the MEAN of 150 seconds and a standard deviation of 25 seconds.  What percentage of the kernels will fail to pop if the popcorn is cooked for <BR>\n" );
document.write( "a) 2 minutes<BR>\n" );
document.write( "b) 3 minutes<BR>\n" );
document.write( "c) if you wanted 95% of the kernels to pop, what time would you allow?<BR>\n" );
document.write( "d) if you wanted 99% to pop<BR>\n" );
document.write( "Thank you<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90997 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=90997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a certain microwave oven on the high power setting, the time it takes a randomly chosen kernel of popcorn to pop is normally distributed with the MEAN of 150 seconds and a standard deviation of 25 seconds. What percentage of the kernels will fail to pop if the popcorn is cooked for <BR>\n" );
document.write( "a) 2 minutes = 120 seconds<BR>\n" );
document.write( "z(120) = (120-150)/25 =-30/25 = -6/5 = -1.2<BR>\n" );
document.write( "P(z>-1.2) = 0.8849<BR>\n" );
document.write( "----------------------- <BR>\n" );
document.write( "b) 3 minutes = 180 seconds<BR>\n" );
document.write( "z(180) = (180-150)/25=30/25 = 6/5 = 1.2<BR>\n" );
document.write( "P(z>1.2) = 0.1151<BR>\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "\n" );
document.write( "c) if you wanted 95% of the kernels to pop, what time would you allow?<BR>\n" );
document.write( "InvNorm(0.95) = 1.645<BR>\n" );
document.write( "Use the formula z(x)=(x-mu)/sigma to find the Raw or X score<BR>\n" );
document.write( "1.645 = (x-150)/25<BR>\n" );
document.write( "x-150 = 25*1.645<BR>\n" );
document.write( "x = 41.12=150 = 191.12 seconds<BR>\n" );
document.write( "x = 3 minutes and 11.12 seconds<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "d) if you wanted 99% to pop<BR>\n" );
document.write( "InvNorm(0.99) = 2.326...<BR>\n" );
document.write( "2.326 = (x-150)/25<BR>\n" );
document.write( "x = 25*2.326+150<BR>\n" );
document.write( "x = 208.16 seconds<BR>\n" );
document.write( "x = 3 minutes 28.16 seconds<BR>\n" );
document.write( "==============================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );