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?
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
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