If you want the exact answer, you can use the Binomial distribution with the following parameters:
P(X < 175) = P(X <= 174) = use binomcdf command on a TI-84 calculator to find that the exact answer is 0.0206
If you wanted to find an approximate answer, you can use a Normal Approximation to the Binomial Distribution with a discrete value to a continuous value adjustment.
Mean = np = 1000(0.2) = 200
Standard Deviation = square root of (npq) = sqrt(1000*.20*..80) = 12.64911064
Then use normalcdf command on the calculator P(X<175) = P(X<=174.5) = normalcdf(lower bound = 0, upper bound = 174.5, mean = 200, standard deviation = 12.64911064) =
The approximate answer is 0.0219
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