In a grand jury case, a bookstore was indicted in Oklahoma County on several cou

Question

In a grand jury case, a bookstore was indicted in Oklahoma County on several counts of selling an obscene book. The grand jury was composed of 22 Baptists and 8 other people. The defendant feels that Baptists are biased against free speech.

(a) What is the probability that 22 or more Baptists are selected on a jury if Oklahoma County is 40% Baptist?

(b) Although the entire population is only 40% Baptist, the population available for jury duty is 60% Baptist. What is the probability that 22 or more Baptists are selected for the jury if the available jury duty population is 60% Baptist?

Explanation / Answer

a) Given information is related to binomial distribution, n = 30, p = 0.4, q = 0.6, and number of successes 'x' = 22

Now normal approximation to the binomial, µ = np = 12

   = npq = 2.683

p [X > 22] = p [Z > 22 - 12 / 2.683]

= p [Z > 3.727]

= 0.0001

b) it is complementary of above event, Required probaility of that 22 or more Baptists are selected for the jury if the available jury duty population is 60% Baptist = 1 - 0.0001 = 0.9999

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