document.write( "Question 1206455: The probability that a certain type of vacuum tube will shatter during a thermal shock test is 0.15. The researches decide to test 80 vacuum tubes.\r
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Algebra.Com's Answer #843961 by ikleyn(52781)\"\" \"About 
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The probability that a certain type of vacuum tube will shatter during a thermal shock test is 0.15.
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\n" ); document.write( "b) What is the standard deviation of the number of vacuum tubes that will shatter?
\n" ); document.write( "c) Suppose that 17 of the 80 vacuum tubes shatter. Would you consider this unusual?
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document.write( "Obvioulsly, the test is a binomial experiment.\r\n" );
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document.write( "(a)  For binomial distribution, the mean is  m = n*p = 80*0.15 = 12.\r\n" );
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document.write( "     It is the ANSWER to (a).\r\n" );
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document.write( "(b)  The standard deviation is  s = \"sqrt%28n%2Ap%2A%281-p%29%29\" = \"sqrt%2880%2A0.15%2A%281-0.15%29%29\" = 3.194  (rounded).\r\n" );
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document.write( "     It is the ANSWER to (b).\r\n" );
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document.write( "(c)  For (c), calculate the probability of this outcome. Use the standard formula for binomial distribution probability\r\n" );
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document.write( "         P = \"C%5B80%5D%5E17%2A0.15%5E17%2A%281-0.15%29%5E%2880-15%29\" = \"1.0149%2A10%5E17%2A0.15%5E17%2A0.85%5E65\" = 0.02583  (rounded).\r\n" );
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document.write( "     So, this probability is quite small.\r\n" );
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document.write( "     Notice that 17 is about 2 standard deviations of 3.1 (each) from the mean of 12, so, it confirms that such event\r\n" );
document.write( "     happens quite rare.\r\n" );
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