A car dealer wants to know with 95% confidence what percentage of the 1500 customers who bought a vehicle from him 5 years ago are still driving it today. In a random sample of 250 customers, it turns out that 207 currently drive a different vehicle.

(a) Identify the correct confidence interval.

(b) What would the confidence interval have to be if the population had been 10,000 customers?

(c) What must the minimum sample size from part (b) be, so that the length of the confidence interval is no more than six percentage points?

(d) What is the maximum number of customers who drive the same car with 95% confidence?

(e) How many customers drive the same car with at least 95% confidence if only 10 of 60 respondents reported doing so?