Answer:
Therefore, there is 0.0062 probability that more than 20% of Americans do not have health insurance.
Step-by-step explanation:
Sixteen percent of Americans do not have health insurance. Suppose a simple random sample of 500.
From the above information,
p = 16% = 0.16
n = 500
The mean is given by
The standard deviation is given by
What is the probability that more than 20% do not have health insurance?
We can use the Normal distribution as an approximation to the Binomial distribution since the following conditions are satisfied.
n×p ≥ 5 (satisfied)
n×(1 - p) ≥ 5 (satisfied)
So the probability is given by
500×0.20 = 100
We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution) to approximate discrete probability distribution (Binomial distribution).
The z-score corresponding to 2.50 is 0.9938
Therefore, there is 0.0062 probability that more than 20% of Americans do not have health insurance.