document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182375>Question 1182375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Precision Scientific Instruments company manufactures thermometers that<BR>\n" );
document.write( "are supposed to read 0<BR>\n" );
document.write( "𝑜𝐶 at the freezing point of water. Tests on these<BR>\n" );
document.write( "instruments revealed that at the freezing point of water some thermometers<BR>\n" );
document.write( "give readings above zero degrees Celsius while other thermometers give<BR>\n" );
document.write( "readings below zero degrees Celsius with an average of zero degrees Celsius<BR>\n" );
document.write( "and a standard deviation of the readings ion 0.9<BR>\n" );
document.write( "𝑜𝐶. Assume that the readings are<BR>\n" );
document.write( "normally distributed,<BR>\n" );
document.write( "i. Find the probability of observing one thermometer at random whose<BR>\n" );
document.write( "reading is between +𝟎. 𝟓𝒐𝑪 and +𝟏. 𝟔𝒐𝑪 at the freezing point of water. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812433 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=812433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = temperature in degrees Celsius<BR>\n" );
document.write( "mu = 0 = population mean temperature in degrees C<BR>\n" );
document.write( "sigma = 0.9 = population standard deviation for the temperatures\r<BR>\n" );
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document.write( "Convert x = 0.5 to a corresponding z score<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (0.5-0)/0.9<BR>\n" );
document.write( "z = 0.56 approximately\r<BR>\n" );
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document.write( "Do the same for x = 1.6<BR>\n" );
document.write( "z = (x-mu)/sigma<BR>\n" );
document.write( "z = (1.6-0)/0.9<BR>\n" );
document.write( "z = 1.78 approximately\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Your teacher is asking you to find P(0.5 < x < 1.6) which is roughly equivalent to P(0.56 < z < 1.78) based on those earlier z score conversions.\r<BR>\n" );
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document.write( "Now use a z table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a> <BR>\n" );
document.write( "or one you would find in the back of your textbook. \r<BR>\n" );
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document.write( "From that table, we see the following approximations<BR>\n" );
document.write( "P(z < 0.56) = 0.71226<BR>\n" );
document.write( "P(z < 1.78) = 0.96246<BR>\n" );
document.write( "which are found as shown below<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" width=\"50%\" src = \"https://i.imgur.com/FPZZT8w.png\"><BR>\n" );
document.write( "the stuff in red pertains to z = 0.56, while the stuff in blue is for z = 1.78\r<BR>\n" );
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document.write( "Then we subtract those values to get the answer we're after<BR>\n" );
document.write( "P(a < z < b) = P(z < b) - P(z < a)<BR>\n" );
document.write( "P(0.56 < z < 1.78) = P(z < 1.78) - P(z < 0.56)<BR>\n" );
document.write( "P(0.56 < z < 1.78) = 0.96246 - 0.71226<BR>\n" );
document.write( "P(0.56 < z < 1.78) = 0.2502<BR>\n" );
document.write( "P(0.5 < x < 1.6) = 0.2502\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "Answer: Approximately 0.2502<BR>\n" );
document.write( "Use a calculator to get more accuracy.\r<BR>\n" );
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document.write( "There's roughly a 25.02% chance of getting a reading between 0.5 degrees C and 1.6 degrees C (when the true reading should be 0 degrees C).<BR>\n" );
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