document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=388626>Question 388626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5) The weight of a newborn is a random variable X which has the standard normal distribution with the mean weight is 3 kg. The standard deviation &#61555; = 0.2 kg. The minimum weight of newborn is 1.5 kg.<BR>\n" );
document.write( "a) Calculate the probability of newborn that has the weight within the interval 3kg to 3.4kg.<BR>\n" );
document.write( "b) The newborn that has the weight less than 2.5kg is deprived of weight. Calculate the probability of newborn that deprived of weight.<BR>\n" );
document.write( "c) The newborns in 10% of the smallest weight need look after careful. Calculate the maximum weight of newborn that need look after careful.<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 #274992 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=274992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The weight of a newborn is a random variable X which has the standard normal distribution with the mean weight is 3 kg. The standard deviation &#61555; = 0.2 kg. The minimum weight of newborn is 1.5 kg.<BR>\n" );
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document.write( "a) Calculate the probability of newborn that has the weight within the interval 3kg to 3.4kg.<BR>\n" );
document.write( "z(3 kg) 0<BR>\n" );
document.write( "z(3.4 kb) = (3.4-3)/1.5 = 0.4/1.5 = 0.267<BR>\n" );
document.write( "P(3< x < 3.4) = P(0< z < 0.267) = 0.1052<BR>\n" );
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document.write( "b) The newborn that has the weight less than 2.5kg is deprived of weight. Calculate the probability of newborn that deprived of weight.<BR>\n" );
document.write( "z(1.5) = (1.5-3)/1.5 = -1<BR>\n" );
document.write( "z(2.5) = (2.5-3)/1.5 = -0.5/(1.5) = -1/3<BR>\n" );
document.write( "P(1.5 < x < 2.5) = P(-1< z <-1/3) = 0.2108<BR>\n" );
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document.write( "c) The newborns in 10% of the smallest weight need look after careful. Calculate the maximum weight of newborn that need look after careful.<BR>\n" );
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document.write( "Find the z-value interval that has that 10% of the population.<BR>\n" );
document.write( "Area below x = 1.5 = Area below z=-1 is 0.1587<BR>\n" );
document.write( "The next 10% interval includes a left-tail of 0.2587 <BR>\n" );
document.write( "The z-value for that left tail is -0.6475<BR>\n" );
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document.write( "Max weight in that interval is : x = zs+u<BR>\n" );
document.write( "x = -0.6475*1.5+3 = 2.0290 kg<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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