document.write( "Question 1200360: A soft drink vending machine is set to discharge an average of 215ml of cool drink per
\n" ); document.write( "cup. The amount discharged is normally distributed with standard deviation 10ml.
\n" ); document.write( "(i) If 250ml cups are used what proportion of cups overflow?
\n" ); document.write( "(ii) What is the probability that a cup contains at least 200ml of cool drink?
\n" ); document.write( "(iii) What size cups ought to be used if it is desirable that only 2% of cups overflow?
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Algebra.Com's Answer #834470 by Shin123(626) $\"\"$ $\"About$

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(i) The z-score of $\"250\"$ is $\"%28250-215%29%2F10=3.5\"$ . We can use a z-table to see that the proportion of cups that don't overflow is $\"0.99977\"$ , so the proportion of cups that do overflow is $\"1-0.99977=0.00023\"$ , or $\"0.023%25\"$
\n" ); document.write( "(ii) The z-score of $\"200\"$ is $\"%28200-215%29%2F10=-1.5\"$ . We can again use a z-table to get $\"0.06681\"$ , which is the probability the cup contains less than 200 ml. So the probability that a cup contains at least 200 ml is $\"1-0.06681=0.93319\"$ .
\n" ); document.write( "(iii) We need to find the value on a z-table that is closest to 0.98, since the z-table gives us the area to the left of the curve. We see that $\"2.05\"$ is the closest, and a $\"2.05\"$ z-score translates to size cups of $\"215%2B10%2A1.05=highlight%28225.5%29\"$ ml. \n" ); document.write( "

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