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ass3 stat

ass3 stat - STAT 2507 Solution-Lab Assignment 3 Fall 2009 1...

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STAT 2507 Solution-Lab Assignment # 3 Fall 2009 1. Suppose that X has a binomial distribution with n =25 and p =0.8. Use minitab to simulate 25 values of X . random 25 c1; binomial 25 0.8. (i) [2] How many of your values are less than 21? 18 (ii) [2] How many of your values are between 21 and 24 inclusive? 7. (iii) If Y has a binomial distribution with n =23 and p =0.8, use the ’cdf’ command, (it gives you the value of P ( Y k )), cdf; binomial 23 0.8. to calculate: P ( Y < 18) = P ( Y 6 17) = 0 . 30531 [2] and P (18 Y 22) = P ( Y 6 22) - P ( Y 6 17) = 0 . 9941 - 0 . 30531 = 0 . 68879 [2] (iv) If you simulate 10000 values of Y , what would be the expected number of values (among the 10000 values) that are less than 18? 10000(0.3053)=3053 [2] 2. Suppose that X has a Poisson distribution with mean μ =25. Use the ’cdf’ command cdf; poisson 25. to calculate: P ( X < 18) = P ( Y 6 17) = 0 . 06048 [2] and P (18 X 22) = P ( Y 6 22) - P ( Y 6 17) = 0 . 31735 - 0 . 06048 = 0 . 25687 [2] The expected number of values (among the 10000 values) that are less than 18 is 10000(0.06048)=604.8 [2] 3. Suppose that Y has a normal distribution with mean μ =35 and variance σ 2 =4. To find P ( Y b ), where b is any fixed constant, use the ’cdf’ command cdf b ; normal 35, 2. To find ’?’ that satisfies P ( Y ?) = a , where a is a fixed know number between 0 and 1, use the ’invcdf’ command 1

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invcdf a; normal 35, 2. To simulate 20 observations from the distribution of Y , and put them in c1, in minitab: random 20 c1; normal 35 2. (i) Use minitab to find the probabilities P ( Y 33) = 0 . 158655 [2], P ( Y > 36) = 1 - P ( Y < 36) = 1 - 0 . 691462 = 0 . 308538 [2], and P (33 Y 36) = 0 . 691462 - 0 . 158655 = 0 . 532807 [2]. (ii) What is the value of c in P ( Y c )= 0.25? 33.65102. [2] (iii) Simulate 20 observations from the distribution of Y and use the ’describe’ command to find the mean, ¯ x , and the standard deviation s for these 20 values. How many of the values fall in the interval ¯ x ± 2 s ? 19 since ¯ x ± 2 s = 35 . 374 ± 2(1 . 92) = (31 . 534 , 39 . 214) [4].
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ass3 stat - STAT 2507 Solution-Lab Assignment 3 Fall 2009 1...

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