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# A04ans - EXERCISES IN STATISTICS Series A No 4 1 Ten jurors...

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EXERCISES IN STATISTICS Series A, No. 4 1. Ten jurors are selected at random from a long list of names of which one third belong to women. The selection is regarded as unsatisfactory if either sex is represented by less than three people. Find the probability that the selection will be unsatisfactory. Answer: The probability of a juror being a woman is 1 / 3. The number x of the women on the jury has a binomial distribution: x b ( x, n =10 ,p = 1 3 ) . The selection is unsatisfactory if x ∈{ 0 , 1 , 2 , 8 , 9 , 10 } , and the probability of this event is b (0) + b (1) + b (2) + b (8) + b (9) + b (10) = ± 2 3 10 +10 ± 1 3 ¶± 2 3 9 + 10 × 9 2 ± 1 3 2 ± 2 3 8 + 10 × 9 2 ± 1 3 8 ± 2 3 2 +10 ± 1 3 9 ± 2 3 + ± 1 3 10 = 17 , 856 59 , 049 3 10 . 2. Assume that the distribution of the heights of adult males is approximately normal with a mean of 69 ins and a standard deviation of 3 ins. What is the conditional probability that an individual will be taller than 72 ins if it is known that he is taller than 70 ins.?

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A04ans - EXERCISES IN STATISTICS Series A No 4 1 Ten jurors...

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