document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309818>Question 309818</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( "This is one question of many on a Statistics quiz due monday night for me. I would greatly appreciate any and all help provided.  Thank you in advance!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221592 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=221592\">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" );
document.write( "a. If you have a body temperature of 99.00 °F, what is your percentile score?<BR>\n" );
document.write( "Find the percent of scores that are below 99.<BR>\n" );
document.write( "z(99) = (99-98.2)/0.62 = 1.2903<BR>\n" );
document.write( "P(x < 99) = P(z < 1.2903) = 0.9015 = 90.15%ile<BR>\n" );
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document.write( "b. Convert 99.00 °F to a standard score (or a z-score). = 1.2903<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( "No; z >= 2 is usually considered to be the cut-off for \"unusual\".<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" );
document.write( "z(97.98) = (97.98-98.2)/[0.62/sqrt(50)] = -2.5091<BR>\n" );
document.write( "P(x-bar <= 97.98) = P(z <= -2.5001) = 0.0061<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" );
document.write( "The z-value is 4.5161<BR>\n" );
document.write( "What do you think?<BR>\n" );
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document.write( "f. What body temperature is the 95th percentile?<BR>\n" );
document.write( "Find the z-value that has a left-tail of 0.95.<BR>\n" );
document.write( "invNorm(0.95) = 1.645<BR>\n" );
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document.write( "Solve for \"x\":<BR>\n" );
document.write( "x = zs+u = 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( "x = -1.645*0.62+98.2 = 97.18 degrees\r<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( "Can you handle \"h\" now?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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