Question

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

If 48 jurors are randomly chosen, calculate the probability that at least half of them will be unfairly prejudicial in this way assuming that the distribution of sample proportions is normal. You may find this standard normal table useful. Give your answer as a decimal to 5 decimal places.

Probability =

Answer 1

Solution

Given that,

p = 0.42

1 - p = 1 - 0.42 = 0.58

n = 48

= p = 0.42

=  [p( 1 - p ) / n] = [(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