SOLUTION: A soft drink vending machine is set to discharge an average of 215ml of cool drink per cup. The amount discharged is normally distributed with standard deviation 10ml. (i) If 250

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Question 1200360: A soft drink vending machine is set to discharge an average of 215ml of cool drink per
cup. The amount discharged is normally distributed with standard deviation 10ml.
(i) If 250ml cups are used what proportion of cups overflow?
(ii) What is the probability that a cup contains at least 200ml of cool drink?
(iii) What size cups ought to be used if it is desirable that only 2% of cups overflow?
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
(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
(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.
(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.