I am having issues solving the following problem:
A recent study found that cedar trees by indigenous settlements grow taller than cedar trees not by indigenous settlements. The probability of a cedar tree being over 90m tall by an indigenous settlement is 0.20. If we take a random sample of 200 cedar trees growing near indigenous settlements, what is the probability that between 25 and 75 trees (exclusive) will be over 90m tall?
Now to start, I can see that N is large (200) and p is small (0.2), so I think this is a good candidate for normal approx. I can verify that np & nq > 5, which confirms this.
I need P(25 < X < 75) and add the continuity correction so
P(25.5 < X < 74.5) = P(X ≤ 74.5) - P(X ≤ 25.5)
μ = np = 40 and σ = 5.657 so to find z scores: (x-μ)/σ
P(Z ≤ 6.10) - P(Z ≤ -2.56)
The issue here is that 6 is a huge Z score! It is not on the table I am given, suggesting I have gone wrong somewhere? Could someone lend a hand?