Answer
0.249
Work Step by Step
Using the $z$ values in the tables, we find:
N=500, p=.05 , q= .95,
μ=np =500*.05=25, σ = $\sqrt npq$=$\sqrt 500*.05*.95$=4.8734
a.
$P(x=29)$ =$ P(28.5\leq x \leq 29.5) $
For x=28.5, z = $\frac{28.5-25}{4.8734}$=0.7182
For x=29.5, z = $\frac{29.5-25}{4.8734}$=0.9234
$P(28.5 \leq x \leq 29.5)$= $P(0.7182\leq z \leq -0.9234)$ =0.8221-0.7637= 0.0457
b.
$P(x \geq 27)$
$P(x \geq 27)$ : z = $\frac{27-25}{4.8734}$ =0.4104
$P(z \geq 0.4104)$ =0.3408
c.
$P(15\leq x \leq 22) $
For x=15, z = $\frac{15-25}{4.8734}$=-2.0520
For x=22, z =$ \frac{22-25}{4.8734}$=-0.6156
$P(15 \leq x \leq 22 )$ = $P(-2.052\leq z \leq -0.6156)$ =0.2691-0.0201= 0.249
