Quality Progress, February 2005, reports on improvements in customer satisfaction and loyalty made by Bank of America. A key measure of customer satisfaction is the response (on a scale from 1 to 10) to the question: "Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?" Here, a response of 9 or 10 represents "customer delight." Suppose that the survey selected 480 customers. Assume that 45% of Bank of America customers would currently express customer delight. That is, assumep= .45.

(a)Find the probability that the sample proportion obtained from the sample of 480 Bank of America customers would be within three percentage points of the population proportion.

That is, findP(.42< p-hat <.48).(Round youranswer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.)

(b)Find the probability that the sample proportion obtained from the sample of 480 Bank of America customers would be within six percentage points of the population proportion.

That is, findP(.39<p-hat<.51). (Round youranswer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.)