First, find the critical value of Z for a 99% confidence interval:

Norm.inv ( 0.995, 0, 1 ) = 2.576

Remember that the margin of error will be given by Z_crit x standard error:

Margin of error = 2.576 x sd/sqrt(n)

Rearrange in terms of n:

sqrt(n) = 2.56 x sd / Margin of error

n = [ 2.56 x 2.3 / 0.14 ] ^2

= 1791

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