document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=927428>Question 927428</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company manufacturing light bulbs claims that an average light bulb lasts 300<BR>\n" );
document.write( "days. A potential customer randomly selects 15 bulbs for testing. The sampled bulbs<BR>\n" );
document.write( "last an average of 290 days, with a standard deviation of 50 days. If the company’s<BR>\n" );
document.write( "claim were true, what is the probability that 15 randomly selected bulbs would have<BR>\n" );
document.write( "an average life of no more than 290 days?\r<BR>\n" );
document.write( "\n" );
document.write( "mean = 300<BR>\n" );
document.write( "P(x &#8804; 290) = P( z < -10/(50/sqrt(15)) =P(z < -.7746) <BR>\n" );
document.write( "Using a TI calculator 0r similarly a Casio fx-115 ES plus<BR>\n" );
document.write( "P(x &#8804; 290) =P(z < -.7746) = normalcdf(-100, -.7746)= .2193 0r 21.93%\r<BR>\n" );
document.write( "\n" );
document.write( "Where did the -100 come from? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562938 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P(x &#8804; 290) =P(z < -.7746) = normalcdf(-100, -.7746)<BR>\n" );
document.write( "normalcdf(-100, -.7746) Gives us the area Under the Normal Curve from (-100 < z < -.7746)<BR>\n" );
document.write( "z-value -100 is used as a place holder, so to speak, as it is so.... far to the left ... that basically ALL the Area <BR>\n" );
document.write( "to the left of z-value -.7746 is then included. Use z-value -1000 if You wish.<BR>\n" );
document.write( "................<BR>\n" );
document.write( ".....Note how far z-value -3 is to the Left, for example<BR>\n" );
document.write( "For the normal distribution: Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  <BR>\n" );
document.write( "Area under the standard normal curve to the left of the particular z is P(z)<BR>\n" );
document.write( "Note: z = 0 (x value: the mean) 50% of the area under the curve is to the left and 50%  to the right<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C200%2C-5%2C5%2C-.5%2C1.5%2C+graph%28400%2C200%2C-5%2C5%2C-.5%2C1.5%2C+exp%28-x%5E2%2F2%29%29%2C+green%28line%281%2C0%2C1%2Cexp%28-1%5E2%2F2%29%29%2Cline%28-1%2C0%2C-1%2Cexp%28-1%5E2%2F2%29%29%29%2Cgreen%28line%282%2C0%2C2%2Cexp%28-2%5E2%2F2%29%29%2Cline%28-2%2C0%2C-2%2Cexp%28-2%5E2%2F2%29%29%29%2Cgreen%28line%283%2C0%2C3%2Cexp%28-3%5E2%2F2%29%29%2Cline%28-3%2C0%2C-3%2Cexp%28-3%5E2%2F2%29%29%29%2Cgreen%28line%28+0%2C0%2C+0%2Cexp%280%5E2%2F2%29%29%29%2Clocate%284.8%2C-.01%2Cz%29%2Clocate%284.8%2C.2%2Cz%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );