4. (a) A coffee dispensing machine is set to discharge on the average 245 ml of coffee into 250 ml cups. Suppose the amo

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4 A A Coffee Dispensing Machine Is Set To Discharge On The Average 245 Ml Of Coffee Into 250 Ml Cups Suppose The Amo 1 (51.2 KiB) Viewed 18 times

4. (a) A coffee dispensing machine is set to discharge on the average 245 ml of coffee into 250 ml cups. Suppose the amount of coffee dispensed is normally distributed with a standard deviation of 7 ml i. Find the proportion of cups that will be averfilled [3 marks i. Determine the size of the cup that should be used so that not more than 5% cups will overflow [3 mars ill. The coffee is sold at $25 per cup. However, the dispenser owner promises $5 refund if a cup contains less than 235 ml colfee. Suppose the cost of coffee Is $15 per cup, find the owner's expected profit per cup (4 marks] (b) The Department of Environment did a study of automobile pollution at a par ticular location in the past ten years. The pollution measurements are found to be normally distributed with the variance of 10. It is also found that the mean pollution index was 112 during the months of April in previous years. During April this year the department took a random sample of seven measurements and the sample mean pollution index was 106. Test the hypothesis that the mean pollution index has been reduced at the 5% level of significance 4 marks (e) In a clinical test with 540 subjects, 63% sbxwed improvement from the old treatment. While in a clinical test with another 630 subjects, 67% showed improvement from the new treatment. Test, at the 2% level of significance, on whether the new treatment preforms better than the old treatment. State any assumption(s)/approximation(s) sed. (6 mars