document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436490>Question 436490</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?<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 #302050 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=302050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  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" );
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document.write( "a. If you have a body temperature of 99.00 °F, what is your percentile score?<BR>\n" );
document.write( "z(99) = (99-98.2)/0.62 = 1.2903<BR>\n" );
document.write( "P(z < 1.2903) = normalcdf(-100,1.2903) = 0.9015<BR>\n" );
document.write( "So, 99.00 F is the 90%ile score<BR>\n" );
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document.write( "b. Convert 99.00 °F to a standard score (or a z-score).<BR>\n" );
document.write( "done above.<BR>\n" );
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document.write( "c. Is a body temperature of 99.00 °F unusual? Why or why not?<BR>\n" );
document.write( "Not unlikely as is is only 1.29 standard deviations above the mean.<BR>\n" );
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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" );
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document.write( "Note: std of all groups of size \"50\" = 0.62/sqrt(50) = 0.0877<BR>\n" );
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document.write( "z(97.98) = (97.98-98.2)/0.0877 = -2.5086<BR>\n" );
document.write( "P(x-bar < 97.98) = P(z < -2.5086) = 0.0198<BR>\n" );
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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" );
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document.write( "Find the z-value using std = 0.62.<BR>\n" );
document.write( "If the temp is at least 2 std above the mean it is unusual.<BR>\n" );
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document.write( "f. What body temperature is the 95th percentile?<BR>\n" );
document.write( "Find the z-value with a left tail of 0.95<BR>\n" );
document.write( "That value is 1.645<BR>\n" );
document.write( "Solve for \"x\" where x = zs+u<BR>\n" );
document.write( "x = 1.645*0.62+98.2 = 99.22 degrees<BR>\n" );
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document.write( "g. What body temperature is the 5th percentile?<BR>\n" );
document.write( "Same procedure but use z = -1.645<BR>\n" );
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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?<BR>\n" );
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document.write( "If you understand a thru g you should be able to answer \"h\" yourself.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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