PTC is a substance that has a strong bitter taste for some people and is tastele

Question

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited. About 66% of Italians can taste PTC, for example. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC. How large a sample must you collect in order to estimate the proportion of PTC tasters to within ±0.02 with 90% confidence?

I thought from the z table we use 1.645 so

(1.645/.02)^2*((.66*(1-.66))= 1518 but it is wrong. pls help

Explanation / Answer

Z*se<=E

1.645*sqrt(p(1-p)/n)<=0.02

(0.66*(1-0.66)/n)=0.0122^2

0.2244<= 0.00014884n

So 1508>=n

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