Question

A sample of 120 is drawn from a population with a proportion equal to 0.50. Determine the probability of observing between 54 and 72 successes.

Answer 1

This is a binomial distribution question with
n = 120
p = 0.5
q = 1 - p = 0.5
This binomial distribution can be approximated as Normal distribution since
np > 5 and nq > 5
Since we know that

x₁ = 54
x₂ = 72
P(X < 54.0 or X > 72.0)=?

This implies that
P(X < 54.0 or X > 72.0) = P(z < -1.0955 or z > 2.1909) = 0.8491
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