Question

Q3. Sixteen percent of Americans do not have health insurance. Suppose a simple random sample of 500 Americans is obtained. In a random sample of 500 Americans, what is the probability that more than 20% do not have health insurance?

Answer 1

Mean = n * P = ( 500 * 0.16 ) = 80
Variance = n * P * Q = ( 500 * 0.16 * 0.84 ) = 67.2
Standard deviation = = 8.1976

20% of 500 = 500 * 0.2 = 100

P ( X > 100 )
Using continuity correction
P ( X > n + 0.5 ) = P ( X > 100 + 0.5 ) = P ( X > 100.5 )

P ( X > 100.5 ) = 1 - P ( X < 100.5 )
Standardizing the value

Z = ( 100.5 - 80 ) / 8.1976
Z = 2.5

P ( Z > 2.5 )
P ( X > 100.5 ) = 1 - P ( Z < 2.5 )
P ( X > 100.5 ) = 1 - 0.9938
P ( X > 100.5 ) = 0.0062