Based on past data, 70% of credit card purchases at a department store are for amounts exceeding $100. Let ????? be a random variable for the proportion of credit card purchases exceeding $100 in a random sample of 100 customers who purchased using credit.(a) What is the approximate sampling distribution (including the mean and the standard deviation) for the sample proportion, ?????? Be sure to justify your answer.(b) What is the probability that less than 65% of the customers in the sample will make their purchases with a credit card?(c) With 95% probability, within what symmetric limits of the population proportion will the sample proportion be expected to fall?

Based on past data, 70% of credit card purchases at a department store are for amounts exceeding $100. Let ????? be a random variable for the proportion of credit card purchases exceeding $100 in a random sample of 100 customers who purchased using credit.(a) What is the approximate sampling distribution (including the mean and the standard deviation) for the sample proportion, ?????? Be sure to justify your answer.(b) What is the probability that less than 65% of the customers in the sample will make their purchases with a credit card?(c) With 95% probability, within what symmetric limits of the population proportion will the sample proportion be expected to fall?