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A random sample of 380 married couples found that 280 had two or more personality preferences...

A random sample of 380 married couples found that 280 had two or more personality preferences in common. In another random sample of 578 married couples, it was found that only 24 had no preferences in common. Let p1 be the population proportion of all married couples who have two or more personality preferences in common. Let p2 be the population proportion of all married couples who have no personality preferences in common.

(a) Find a 90% confidence interval for p1p2. (Use 3 decimal places.)

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