document.write( "Question 1160672: The times a teacher takes to grade one page of an exam are normally distributed with a mean of 4 minutes and a standard deviation of 1 minute. For about what percent of exams does a teacher grade one page in less than 7 minutes?
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Algebra.Com's Answer #852041 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The times a teacher takes to grade one page of an exam are normally distributed with a mean of 4 minutes
\n" ); document.write( "and a standard deviation of 1 minute. For about what percent of exams does a teacher grade one page
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document.write( "Notice that in this problem 7 minutes time interval is 3 minutes greater than 4 minutes, the average time.\r\n" );
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document.write( "So, apply the empirical rule for normal distribution, which says that 99.7% of data fall into three\r\n" );
document.write( "standard deviations from the mean.\r\n" );
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document.write( "Using this rule, we account 50% for checking exams faster than 4 minutes, and add to it  \r\n" );
document.write( " = 49.85% for the exams to check them from 4 minutes to 7 minutes.\r\n" );
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document.write( "Thus the answer to the question is  50% + 49.85% = 99.85%.    <<<---=== ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely.\r
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\n" ); document.write( "\n" ); document.write( "By the way, out of curiosity, I submitted this problem to Google AI today (07/14/2025).\r
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\n" ); document.write( "\n" ); document.write( "It produced wrong solution, saying that the answer is 99.7%.\r
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\n" ); document.write( "\n" ); document.write( "So, although the problem is very simple, AI could not solve it correctly - - - and failed.\r
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\n" ); document.write( "\n" ); document.write( "It is because this version AI, actually, can not think, in usual meaning of this word.
\n" ); document.write( "It only can re-write a prototype of a solution from a template
\n" ); document.write( "in its base of knowledge, if it will find an appropriate template there.
\n" ); document.write( "But in this case, it could not find an appropriate template - - - and failed.\r
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\n" ); document.write( "\n" ); document.write( "It is what I always say about the current version of AI in solving school Math problems: \r
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\n" ); document.write( "\n" ); document.write( " - it works perfectly, if it finds a template with a correct solution to re-write from.\r
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\n" ); document.write( "\n" ); document.write( "If it will not find such a template - it fails.\r
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\n" ); document.write( "\n" ); document.write( "Naturally, I informed Google AI about their fault in this problem via their feedback system
\n" ); document.write( "and provided the link to this correct solution. So, from now this Google AI is a bit smarter than it was before.\r
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\n" ); document.write( "\n" ); document.write( "Next day, 07/15/25, I checked Google AI by posting this problem again.\r
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\n" ); document.write( "\n" ); document.write( "This time, it created a correct solution, so I am satisfied now.\r
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