About two out of every three gas purchases at Cheap Gas station are paid for by credit cards. 350 customers buying gas at this station are randomly selected. Find the following probabilities using both the normal approximation to the binomial distribution with continuity correction and the binomial distribution.
(a) Find the probability that greater than 210 will pay for their purchases using credit card.
(b) Find the probability that between 120 to 210 will pay for their purchases using credit card.
(c) What are the mean value and standard deviation of the number who pay for their purchases using credit card?
(d) Generate 1000 samples of size 350 from a Binomial distribution with probability 2/3. Calculate the mean and standard deviation of the 1000 samples, and compare to the results in (c).
(e) Plot the density of the sample in (d), and compare it to the curve of Normal distribution with mean and standard deviation in (c).