Question

given: N=250 n=100 μ=35.6 σ=4.89

find: p( ≥36)

Answer 1

When samples are drawn from finite population

$$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}\sqrt{\dfrac{N-n}{N-1}}}$$

$$z=\dfrac{36-35.6}{\dfrac{4.89}{\sqrt{100}}\sqrt{\dfrac{250-100}{250-1}}}=1.053914$$

$$P(X\geq36)=1-P(X<36)$$

$$\approx1-P(Z\leq1.053914)$$

$$\approx0.145961$$