According to studies done in the 1940s, 29% of people dream in color. Assuming this is still true, researchers obtained a random sample of 200 adults to study this further.
(a) Demonstrate that all necessary assumptions for the Central Limit Theorem have been satisfied with this scenario. Use the language of this class and complete sentences.
(b) Find the probability that in a random sample of 200 independent people, 40% or more will report dreaming in color. (Round your answer to three decimal places.