In a recent Gallup poll, american citizens were asked if their standard of living was getting better. assume that 35% of all Americans would say their standard of living is getting better. suppose 8 Americans are randomly selected and asked if they think their standard of living is getting better. make the case that this situation can be modeled by a binomial random variable.

a. Make the case that this situation can be modeled by a binomial random variable.

b. Draw the probability histogram for the binomial random variable (also list the probability measures for each value of X.) Compute the mean and standard deviation of X. Mark where the mean is on the probability histogram and mark the places that are one standard deviation from the mean.

c. What is the probability that X (the number of Americans among the 8 selected who would say their standard of living is getting better) is within one standard deviation of its mean?

d. Continuing from the previous page, what if a sample of 80 Americans are randomly sampled and asked if they think their standard of living is getting better. What is the probability that the sample proportion who say they think their standard of living is getting better is between .30 and .40?