Question

An article reported that 6% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.

(e) When n = 300, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.07?

Answer 1

Solution

Given that,

p = 0.06

1 - p = 1 - 0.06 = 0.94

n = 300

= p = 0.06

=  [p( 1 - p ) / n] = [(0.06 * 0.94 ) / 300 ] = 0.0137

P( > 0.07) = 1 - P( < 0.07 )

= 1 - P(( - ) / < (0.07 - 0.06) / 0.0137)

= 1 - P(z < 0.73)

Using z table

= 1 - 0.7673

= 0.2327