document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1117595>Question 1117595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The shape of the distribution of the time required to get an oil change at a 15<BR>\n" );
document.write( "&#8203;-minute <BR>\n" );
document.write( "&#8203;oil-change facility is unknown.&#8203; However, records indicate that the mean time is 16.2 minutes<BR>\n" );
document.write( "&#8203;, <BR>\n" );
document.write( "and the standard deviation is 3.5 minutes<BR>\n" );
document.write( ".<BR>\n" );
document.write( "&#8203;(a) To compute probabilities regarding the sample mean using the normal&#8203; model, what size sample would be&#8203; required?<BR>\n" );
document.write( "&#8203;(b) What is the probability that a random sample of nequals<BR>\n" );
document.write( "45 <BR>\n" );
document.write( "oil changes results in a sample mean time less than 15<BR>\n" );
document.write( " <BR>\n" );
document.write( "&#8203;minutes?<BR>\n" );
document.write( "&#8203;(a) Choose the required sample size below.<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "The sample size needs to be greater than 30.<BR>\n" );
document.write( "Your answer is correct.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "The normal model cannot be used if the shape of the distribution is unknown.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "The sample size needs to be less than 30.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( "Any sample size could be used.<BR>\n" );
document.write( "&#8203;(b) The probability is approximately nothing<BR>\n" );
document.write( ".<BR>\n" );
document.write( "&#8203;(Round to four decimal places as&#8203; needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733255 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=733255\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Most statisticians will say that as large a sample as one can get, but n=30 has been used because even a t-distribution will be within 2 per cent of normality.<BR>\n" );
document.write( "t(df=44)=(xbar-mean)/s/sqrt(n)<BR>\n" );
document.write( "=(15-16.2)/3.5/sqrt(45)<BR>\n" );
document.write( "=-1.2*sqrt(45)/3.5<BR>\n" );
document.write( "=-2.30<BR>\n" );
document.write( "This is a probability of 0.0130 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );