document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197054>Question 1197054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 28% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)<BR>\n" );
document.write( "a)At what psi will the TPMS trigger a warnig for this car? (Round your answer to 2 decimal points.)\r<BR>\n" );
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document.write( "b)Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( "c)The manufacturer's recommended correct inflation range is 30 psi to 34 psi. Assume the tire's average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recomended range? (Round your intermediate calculations and final answer to 4 decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830149 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a)At what psi will the TPMS trigger a warnig for this car? (Round your answer to 2 decimal points.)\r<BR>\n" );
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document.write( "target pressure = 32 psi.<BR>\n" );
document.write( "28% below 32 = (1 - .28) * 32 = 23.04 psi.<BR>\n" );
document.write( "when the target pressure gets below that, the tpms will warn the driver.\r<BR>\n" );
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document.write( "b)Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 3 psi. If the car's average tire pressure is on target, what is the probability that the TPMS will trigger a warning? (Round your answer to 4 decimal places.)\r<BR>\n" );
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document.write( "with a mean of 32 and a standard deviation of 3, the probability that the tpms will trigger a warning will be based on the following formula.<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard deviation.<BR>\n" );
document.write( "when x = 23.04 and m = 32 and s = 3, the formula becomes:<BR>\n" );
document.write( "z = (23.04 - 32) / 3 = -2.9867 rounded to 4 decimal places.<BR>\n" );
document.write( "probability of getting a z-score less than that is equal to .0014.\r<BR>\n" );
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document.write( "c)The manufacturer's recommended correct inflation range is 30 psi to 34 psi. Assume the tire's average psi is on target. If a tire on the car is inspected at random, what is the probability that the tire's inflation is within the recommended range? (Round your intermediate calculations and final answer to 4 decimal places.)\r<BR>\n" );
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document.write( "z-score for psi of 30:<BR>\n" );
document.write( "z = (30 - 32) / 3 = -.6667 rounded to 4 decimal places.<BR>\n" );
document.write( "z-score for psi of 45:<BR>\n" );
document.write( "z = (34 - 32) / 3 = .6667 rounded to 4 decimal places.<BR>\n" );
document.write( "probability of getting a z-score less than -.6667 is equal to .2525 rounded to 4 decimal places.<BR>\n" );
document.write( "probability of getting a z-score less than .6667 is equal to .7475 rounded to 4 decimal places.<BR>\n" );
document.write( "probability of getting a z-score between -.6667 and .6667 is equal to .7475 minus .2524 = .4950.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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