According to a survey about conspiracy​ theories, about 3​% of adults in a certain country believe that​ shape-shifting reptilian people control our world by taking on human form and gaining power. Assume​ that's the actual proportion of adults in the country who hold that belief. Complete parts a through e below.
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Part 1
​a) Use a Binomial model to calculate the probability​ that, in a sample of 200 ​adults, at least 4​% of those in the sample believe the thing about reptilian people controlling our world.
.254 ​(Round to three decimal places as​ needed.)
Part 2
​b) Now use a Normal model to compute that probability. How does this compare to the answer from part​ a?
Using the Normal​ model, the probability is .203
​(Round to three decimal places as​ needed.)
Part 3
The difference between the two probabilities is . 051.
​(Round to three decimal places as​ needed.)
Part 4
​c) That same poll found that 59​% of adults believe there was a larger conspiracy responsible for the assassination of a certain politician. Use a Binomial model to calculate the probability​ that, in a random sample of 200 ​adults, at least 64​% of those in the sample believe in this conspiracy theory.
. 085 ​(Round to three decimal places as​ needed.)
Part 5
​d) Now use a Normal model to compute that probability. How does this compare to the answer from part​ c?
Using the Normal​ model, the probability is enter your response here.