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1. According to studies done in the 1940's, 29% of people dream in color. Suppose we take a sample of 200 people.

A) Does situation satisfy CLT? Explain using complete sentences.

B) Draw and label the distribution of the sample proportion.

C) Assuming that it is still true that 29% of people dream in color, find the probability that in a random sample of 200 independent people, 35% or more will report dreaming in color.

D) Find the probability that in our sample of 200 people, more than 50% of the people dream in color.

E) Suppose we increased our sample size to 500 people. Without doing any calculations, what do you expect to happen to the probabilities we calculated in C and D? Why?