Question

The random variable Z has a standard normal distribution. Find the value of b if

1) P(b<Z<2.133)=0.1618

Answer 1

$$P(b<Z<2.133)=P(Z<2.133)-P(Z\leq b)$$

$$\approx0.9835-P(Z\leq b)=0.1618$$

$$P(Z\leq b)\approx0.8217$$

$$b\approx0.922$$