Answer
.2229
Work Step by Step
We find:
N=200, p=.80 , q= .20,
μ=np =200*.80=160, σ = $\sqrt npq$=$\sqrt 100*.80*.20$=5.6569
a. P(x= 150) = $P(149.5 \leq x \leq 150.5 )$ = $P(\frac{149.5-160}{5.6569} \leq z \leq \frac{150.5-160}{5.6569})$ =$P(-1.856\leq z \leq -1.679 )$ =0.0465-0.0317= 0.0148
b. $P(x \geq 170)$ : z = $\frac{170-160}{5.6569}$ =$P(z \geq 1.7678)$ = 0.0386
c. $P(x \leq 165)$ : z = $\frac{165-160}{5.6569}$ =$P(z \leq 0.8839)$ = 0.8116
d. $P(164\leq x \leq 172 )$ = $P(\frac{164-160}{5.6569} \leq z \leq \frac{172-160}{5.6569})$ =$P(0.7071 \leq z \leq 2.1213 )$ =0.9831-.7602= 0.2229
