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# A10ans - EXERCISES IN STATISTICS Series A No 10 1 A...

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EXERCISES IN STATISTICS Series A, No. 10 1. A horticulturist considers that a batch of seeds is worth sowing if 50% of the resulting flowers are going to be pure white. To test the worth of a particular batch, he sows eight seeds with the intention of sowing the remainder if at least four of the eight plants have white flowers. Find the probability of his making a wrong decision (a) if 25% of the seeds are of the white variety, and (b) if 75% of the seeds are of the white variety. Answer Let p be the probability that a seed selected at random will produced a white flower, and let x be the number of white flowers in the test sample of n = 8 seeds. We may assume that x b ( n, p ) = n ! ( n x )! x ! p x (1 p ) n x . (a) Let p = 1 / 4. The wrong decision, which is to sow the seeds, is made if x { 4 , 5 , 6 , 7 , 8 } . Observe that P ( x { 4 , 5 , 6 , 7 , 8 } ) = 1 P ( x { 0 , 1 , 2 , 3 , } ). Then P ( x { 0 , 1 , 2 , 3 } ) = 3 X x =0 n ! ( n x )! x ! p x (1 p ) n x = µ 3 4 8 + 8 µ 1 4 ∂ µ 3 4 7 + 8 . 7 2 . 1 µ 1 4 2 µ 3 4 6 + 8 . 7 . 6 3 . 2 . 1 µ 1 4 3 µ 3 4 5 = µ 1 4 8 n 3 8 + 8 . 3 7 + 4 . 7 . 3 6 + 8 . 7 . 3 5 o .

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A10ans - EXERCISES IN STATISTICS Series A No 10 1 A...

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