Answer
0.049
Work Step by Step
We have $p=0.05, n=500$
Check $np=25\gt5, n(1-p)=475\gt5$
Use the normal approximation to the binomial distribution.
$\mu=np=25, \sigma=\sqrt {np(1-p)}=4.87$
Use $X1=29.5,X2=30.5$
we have $z1=\frac{29.5-25}{4.87}=0.924, z2=\frac{30.5-25}{4.87}=1.13$
The probability between z1 and z2 is 0.049
