document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092748>Question 1092748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> suppose that the weiht of mangoes is normally distributed with mean 8 ounces and standard deviation is 1.5 ounces. <BR>\n" );
document.write( "a)what proportion of mangoes weigh more than 11.5 ounces<BR>\n" );
document.write( "b.what proportiion of mangoes weith less than 8.7 ounces.<BR>\n" );
document.write( "c. what proportion of mangoes weith less than 5 ounces<BR>\n" );
document.write( "d.what proportion of mangoes weith more than 4.9 ounces<BR>\n" );
document.write( "e. what proportion of mangoes weith between 6.2 and 7 ounces<BR>\n" );
document.write( "f. what proportion of mangoes weith between 10.3 and 14 ounces<BR>\n" );
document.write( "g. what proportion of mangoes weith between 6.8and 8.9 ounces<BR>\n" );
document.write( "h. find the 80th percentile of the distribution of x.<BR>\n" );
document.write( "i. find the 5th percentile of the distribution of x.<BR>\n" );
document.write( "j. find the interquartile range of the distribution of x.<BR>\n" );
document.write( "show your working and formulas tx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707367 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The basic formula is z=(x=mean)/std deviation.<BR>\n" );
document.write( "a. z=(11.5-8)/1.5 so z=2.33.  Want z > 2.33 From calculator or table, this probability is 0.0099.<BR>\n" );
document.write( "b. z is less than .7/1.5 or 0.47.  This is a probability of 0.3192.<BR>\n" );
document.write( "c.  z is -3/1.5 or z is less than -2, with probability of 0.0228<BR>\n" );
document.write( "d. z is greater than -3.1/1.5=z is greater than -2.07 or probability 0.9808<BR>\n" );
document.write( "e. this is a z between -1.8/1.5 and -1/1.5; this is -1.2<z<-0.67 or probability of 0.1364<BR>\n" );
document.write( "f. this is a z between 2.3/1.5 and 4 or  probability of 0.0626<BR>\n" );
document.write( "g.  this is a z between -1.2/1.5 and +0.9/1.5 or between -0.8 and +0.6 or probability of 0.5139<BR>\n" );
document.write( "h. 80th percentile is where z is +0.84, so that (x-mean)/1.5=0.84 or (x-mean=1.26), or x=mean+1.26, so that x=9.26 oz.<BR>\n" );
document.write( "i.  5th percentile is z=-1.645, and x-mean = -2.47 so that x=8-2.47 or 5.53 oz.<BR>\n" );
document.write( "j. interquartile is z.25 and z.75 which is -0.675 to +0.675 for z or +/- 1.01 oz from the mean or (6.99, 9.01).  The +/- 1.01 is z* sd.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );