Opinion polls find that 20% of American adults claim they never have time to relax. Suppose you take a random sample of 200 American adults, and you count the number X in your sample that claim they never have time to relax. Using the Normal approximation, the probability that X is at least 50 is:

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The sample size (n=200) is large enough for us to use the Normal approximation. We can model the number X of individuals who claim they never have time to relax with a normal distribution with mean μ = np and standard deviation σ = sqrt(np(1-p)), where n=200 and p=0.2.
Thus, X ~ N(μ=40, σ=4.00).
To find the probability that X is at least 50, we can standardize X:
Z = (50 - 40)/4.00 = 2.50
And we can find the probability using a standard normal table or calculator as P(Z ≥ 2.50) = 0.0062.
Therefore, the answer is D) about 0.038.

Opinion Polls Find That 20% of American Adults Claim They