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Unformatted text preview: Stat 211 - Tutorial 4 SOlutions/Answers Questions are adapted from the book titled "A concise course in advanced level statis- tics: with worked examples" by J. Crawshaw and J. Chambers. 1. (a) 0.2927 (b) 420.40ml 2. A machine is used to fill tubes, of nominal content 100 ml, with toothpaste. The amount of toothpaste delivered by the machine is normally distributed and may be set to any required mean value. Immediately after the machine has been over- hauled, the standard deviation of the amount delivered is 2 ml. As time passes, this standard deviation increases until the machine is again overhauled. The following three conditions are necessary for a batch of tubes of toothpaste to comply with current legislation: I: the average content of the tubes must be at least 100 ml, II: not more than 2.5% of the tubes may contain less than 95.5 ml, III: not more than 0.1% of the tubes may contain less than 91 ml. (a) For a batch of tubes with mean content 98.8 ml and standard deviation 2 ml, find the proportion of tubes which contain i. less than 95.5 ml, Solution : Let X = amount of toothpaste in a tube (in ml). Then X G (98 . 8 , 2) . We require P ( X < 95 . 5) = P X- 98 . 8 2 < 95 . 5- 98 . 8 2 = P ( Z <- 1 . 65) = 0 . 0495 ii. less than 91 ml. Solution : Using the above definition of X , we require P ( X < 91) = P X- 98 . 8 2 < 91- 98 . 8 2 = P ( Z <- 3 . 9) = 0 . 0001987 This value is not shown in the table. The minimum value of z that is pro- vided is z =- 3 . 49 . If you were to use the table, the most you can do is....
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