# A jury is to be selected for a

A jury is to be selected for a proceeding in which the accusedis alleged to have stolen money from a business partner. Accordingto existing data, 42% of potential jurors have been a victim of amajor theft at some point in their life that will make themunfairly prejudicial against the accused.

If 48 jurors are randomly chosen, calculate the probability thatat least half of them will be unfairly prejudicial in this wayassuming that the distribution of sample proportions is normal. Youmay find this standard normal table useful. Give your answer as adecimal to 5 decimal places.

Probability =

Solution

Given that,

p = 0.42

1 – p = 1 – 0.42 = 0.58

n = 48

= p = 0.42

=  $\sqrt$[p(1 – p ) / n] = $\sqrt$[(0.42 * 0.58) / 48 ] = 0.0712

P(   0.5) = 1 – P( 0.5 )

= 1 – P(( ) /   (0.5 – 0.42) / 0.0712)

= 1 – P(z 1.1236)

Using z table

= 1 – 0.86860

= 0.13140

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