First, find the critical value of Z for a 90% confidence interval:

Norm.inv ( 0.95, 0, 1 ) = 1.64

Standard deviation is sqrt(variance) = sqrt(34.81) = 5.90

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

Margin of error = 1.64 x sd/sqrt(n)

Rearrange in terms of n:

sqrt(n) = 1.64 x sd / Margin of error

n = [ 1.64 x 5.90 / 0.37 ] ^2

= 688

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