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**Unformatted text preview: **THE UNIVERSITY OF SYDNEY Math1005 Statistics Semester 2 Tutorial Week 5 2006 1. Of a large (effectively infinite) number of mass-produced articles, it is known that one tenth are defective. Writing X for the number of defective items in a random sample of 8 of these articles, explain why X has a binomial distribution. 2. ( Multiple choice ) Writing the distribution of X in Q1 as X ∼ B ( n, p ), the values of n and p are: (a) 10 and 8 (b) 0.1 and 8 (c) 8 and 0.1 (d) 8 and 1 (e) ∞ and 5. 3. ( Multiple choice ) For the binomial random variable in Q2, P ( X ≤ 2) is: (a) 0.9950 (b) 0.8131 (c) 0.7969 (d) 0.9619 (e) -0.9619 4. Suppose that X is binomial B (10 , . 4). Write down an expression for P ( X = i ) for 0 ≤ i ≤ 10. Calculate P ( X ≤ 1) and P ( X < 3) directly. Verify your answers using binomial tables. Also use binomial tables to find P ( X ≤ 4), and P ( X > 3). 5. From previous experiments it is found that 40% of the mice used in an experiment become very aggressive within one minute of being administered an experimental drug. Using thevery aggressive within one minute of being administered an experimental drug....

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