Question 1160672
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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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<pre>
Notice that in this problem 7 minutes time interval is 3 minutes greater than 4 minutes, the average time.


So, apply the empirical rule for normal distribution, which says that 99.7% of data fall into three
standard deviations from the mean.


Using this rule, we account 50% for checking exams faster than 4 minutes, and add to it  
{{{99.7/2}}} = 49.85% for the exams to check them from 4 minutes to 7 minutes.


Thus the answer to the question is  50% + 49.85% = 99.85%.    <<<---=== <U>ANSWER</U>
</pre>

At this point, the problem is solved completely.



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By the way, out of curiosity, I submitted this problem to Google AI today (07/14/2025).


It produced wrong solution, saying that the answer is 99.7%.


So, although the problem is very simple, AI could not solve it correctly - - - and failed.


It is because this version AI, actually, can not think, in usual meaning of this word.
It only can re-write a prototype of a solution from a template 
in its base of knowledge, if it will find an appropriate template there.
But in this case, it could not find an appropriate template - - - and failed.



It is what I always say about the current version of AI in solving school Math problems: 


&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- it works perfectly, if it finds a template with a correct solution to re-write from.


If it will not find such a template - it fails.



Naturally, I informed Google AI about their fault in this problem via their feedback system
and provided the link to this correct solution. So, from now this Google AI is a bit smarter than it was before.



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Next day, 07/15/25, I checked Google AI by posting this problem again.


This time, it created a correct solution, so I am satisfied now.