document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=314444>Question 314444</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers).<BR>\n" );
document.write( "a.	If you have a body temperature of 99.00 °F, what is your percentile score?<BR>\n" );
document.write( "b.	Convert 99.00 °F to a standard score (or a z-score).<BR>\n" );
document.write( "c.	Is a body temperature of 99.00 °F unusual? Why or why not?<BR>\n" );
document.write( "d.	Fifty adults are randomly selected. What is the likelihood that the mean of their body temperatures is 97.98 °F or lower?<BR>\n" );
document.write( "e.	A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude?<BR>\n" );
document.write( "f.	What body temperature is the 95th percentile?<BR>\n" );
document.write( "g.	What body temperature is the 5th percentile?<BR>\n" );
document.write( "h.	Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #224974 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=224974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=98.20 ALIGN=MIDDLE  ALT=\"mu=98.20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=0.62 ALIGN=MIDDLE  ALT=\"sigma=0.62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=99 ALIGN=MIDDLE  ALT=\"x=99\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x-mu%29%2Fsigma=%2899-98.2%29%2F0.62=1.33 ALIGN=MIDDLE  ALT=\"z=%28x-mu%29%2Fsigma=%2899-98.2%29%2F0.62=1.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%281.33%29=0.9087 ALIGN=MIDDLE  ALT=\"P%281.33%29=0.9087\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "91st percentile.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ". <BR>\n" );
document.write( "b. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1.33 ALIGN=MIDDLE  ALT=\"z=1.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( ".<BR>\n" );
document.write( "c. Depends on what you consider normal, unusual, etc., you should make that determination and be able to defend your position. <BR>\n" );
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document.write( "d. Set up a t test.<BR>\n" );
document.write( "The null hypothesis is that the means are the same. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=50 ALIGN=MIDDLE  ALT=\"N=50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=X=97.98 ALIGN=MIDDLE  ALT=\"X=97.98\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=sigma%2Fsqrt%28N-1%29=0.62%2Fsqrt%2850-1%29=0.62%2F7=0.00886 ALIGN=MIDDLE  ALT=\"S=sigma%2Fsqrt%28N-1%29=0.62%2Fsqrt%2850-1%29=0.62%2F7=0.00886\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28X-mu%29%2FS=%2897.98-98.2%29%2F0.00886=-2.484 ALIGN=MIDDLE  ALT=\"t=%28X-mu%29%2FS=%2897.98-98.2%29%2F0.00886=-2.484\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the challenge is in working out the critical t value. <BR>\n" );
document.write( "t(0.05,49)=1.647<BR>\n" );
document.write( "t(0.01,49)=2.405<BR>\n" );
document.write( "Depending on the critical t value you choose, you could reject the null hypothesis, in which case, you would say the means are not the same, there is a statistically significant difference in the findings. <BR>\n" );
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document.write( "e. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=101 ALIGN=MIDDLE  ALT=\"x=101\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x-mu%29%2Fsigma=%28101-98.2%29%2F0.62=4.52 ALIGN=MIDDLE  ALT=\"z=%28x-mu%29%2Fsigma=%28101-98.2%29%2F0.62=4.52\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%284.52%29=0.999998 ALIGN=MIDDLE  ALT=\"P%284.52%29=0.999998\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Yes, that would be odd because very few people would normally have that temperature. <BR>\n" );
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document.write( "f. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=0.95 ALIGN=MIDDLE  ALT=\"P%28z%29=0.95\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=1.645=%28x-98.2%29%2F0.62 ALIGN=MIDDLE  ALT=\"z=1.645=%28x-98.2%29%2F0.62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=99.2 ALIGN=MIDDLE  ALT=\"x=99.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "g. What body temperature is the 5th percentile?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=0.05 ALIGN=MIDDLE  ALT=\"P%28z%29=0.05\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=-1.645=%28x-98.2%29%2F0.62 ALIGN=MIDDLE  ALT=\"z=-1.645=%28x-98.2%29%2F0.62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=97.2 ALIGN=MIDDLE  ALT=\"x=97.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "h. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28x-mu%29%2Fsigma=%28100.6-98.2%29%2F0.62=1.33 ALIGN=MIDDLE  ALT=\"z=%28x-mu%29%2Fsigma=%28100.6-98.2%29%2F0.62=1.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28z%29=0.999968 ALIGN=MIDDLE  ALT=\"P%28z%29=0.999968\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Normally and healthy would be ones who have higher than 100.6 but are not sick.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=1-0.999968=0.000032 ALIGN=MIDDLE  ALT=\"P=1-0.999968=0.000032\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "That's pretty low, so you would think it's pretty unlikely that someone coming in off the street would have a 100.6 temperature and be normal. The cutoff is probably appropriate. Again check the caveats in section c. </SPAN>\n" );
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