Question

a biologist estimates that 50% of deer in the region carry a certain type of tick. for a sample of 300 deer selected at random, what is the chance that 155 or fewer deer have this tick?

Answer 1

$p=0.5 , \hat{p}=\dfrac{155}{300}=0.516,n=300$

Probability that 155 or fewer deer has a tick-

$=P(z\le\dfrac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}})\\[9pt]=P(z\le \dfrac{0.516-0.5}{\sqrt{\frac{0.5(1-0.5)}{300}}})\\[9pt]=P(z\le 0.554)\\[9pt]=0.69387$