Selection of trial juries occurs in two stages: a venire panel is chosen, then j

Question

Selection of trial juries occurs in two stages: a venire panel is chosen, then jury of 12 is selected from that panel. This problem considers the rst stage, selection of the venire panel. In the 1967 Supreme Court case 385 US 545, a black petitioner appealed conviction, claiming that blacks had unconstitutionally been excluded from the venire panel. The state asserted that the 90 person venire panel had been randomly drawn from an extensive tax list on which 27% of the persons were black. The actual venire panel contained only seven black persons. Assuming that we can model this using a binomial experiment with probability of success 0.27 and 90 trials, nd the probability that a genuinely random selection of 90 names from the tax list would contain at most seven black names.

Explanation / Answer

Let x be the number of black names..

p = 0.27, n = 90

x follows Binomial distribution with p = 0.27 and n = 90

We have to find at most seven black names in randomly selected 90 names.

That is P( x <= 7 )

Using Excel,

P( x <= 7 ) = BINOMDIST( 7, 90,0.27,1 )=0.0000045

Probability that a genuinely random selection of 90 names from the tax list would contain at most seven black names is 0.0000045

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