document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=460443>Question 460443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> at a hospital maternity ward,<BR>\n" );
document.write( " the hospital staff wants a probability distribution for the number of babies arriving each hour.<BR>\n" );
document.write( "what is the probability exactly 7 babies are born during the next hour?<BR>\n" );
document.write( "what is the probability than fewer than 3 babies are born during the next hour? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #315825 by </B><A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><B>Tatiana_Stebko(1539)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Tatiana_Stebko><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=Tatiana_Stebko><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=315825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the expected number of occurrences in this interval is a, then theprobability that there are exactly k occurrences is equal to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28k%2Ca+%29=%28%28a%5Ek%29e%5E%28-a%29%29%2Fk%21 ALIGN=MIDDLE  ALT=\"P%28k%2Ca+%29=%28%28a%5Ek%29e%5E%28-a%29%29%2Fk%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where<BR>\n" );
document.write( "e is the base of the natural logarithm (e = 2.71828...)<BR>\n" );
document.write( "k is the number of occurrences of an event — the probability of which is given by the function<BR>\n" );
document.write( "k! is the factorial of k<BR>\n" );
document.write( "a is a positive real number, equal to the expected number of occurrences during the given interval. \r<BR>\n" );
document.write( "\n" );
document.write( "Babies arrive at an average of 8 babies per hour, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=8 ALIGN=MIDDLE  ALT=\"a=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1) what is the probability exactly 7 babies are born during the next hour?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=7 ALIGN=MIDDLE  ALT=\"k=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%287%2C8+%29=%28%288%5E7%29e%5E%28-8%29%29%2F7%21=0.1396 ALIGN=MIDDLE  ALT=\"P%287%2C8+%29=%28%288%5E7%29e%5E%28-8%29%29%2F7%21=0.1396\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2) what is the probability that fewer than 3 babies are born during the next hour?<BR>\n" );
document.write( "Fewer than 3 - means that 0 babies (k=0) or 1 baby (k=1) or 2 babies (k=2) are born during the next hour<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28fewer+than+3%29=P%280%2C8%29%2BP%281%2C8%29%2BP%282%2C8%29 ALIGN=MIDDLE  ALT=\"P%28fewer+than+3%29=P%280%2C8%29%2BP%281%2C8%29%2BP%282%2C8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28fewer+than+3%29=%28%288%5E0%29e%5E%28-8%29%29%2F0%21%2B%28%288%5E1%29e%5E%28-8%29%29%2F1%21%2B%28%288%5E2%29e%5E%28-8%29%29%2F2%21=0.0003%2B0.0027%2B0.0107=0.0137 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );