Question

use this table or the aleks calculator to complete the following. give your answers to four decimal places (for example, 0.1234). (a) find the area under the standard normal curve to the right of z = 0.85. (b) find the area under the standard normal curve between z = - 1.81 and z = 0.73.

Explanation:

Step1: Recall standard - normal table property for part (a)

The total area under the standard - normal curve is 1. The area to the left of $z = 0.85$ can be found from the standard - normal table. Let $\Phi(z)$ be the cumulative - distribution function of the standard - normal distribution. The area to the right of $z = 0.85$ is $1-\Phi(0.85)$. Looking up $\Phi(0.85)$ in the standard - normal table, we find $\Phi(0.85)=0.8023$. So the area to the right is $1 - 0.8023=0.1977$.

Step2: Recall standard - normal table property for part (b)

The area under the standard - normal curve between $z_1=-1.81$ and $z_2 = 0.73$ is $\Phi(0.73)-\Phi(-1.81)$. Since the standard - normal distribution is symmetric about $z = 0$, $\Phi(-z)=1 - \Phi(z)$. So $\Phi(-1.81)=1-\Phi(1.81)$. Looking up $\Phi(0.73)=0.7673$ and $\Phi(1.81)=0.9649$, then $\Phi(-1.81)=1 - 0.9649 = 0.0351$. The area between $z=-1.81$ and $z = 0.73$ is $\Phi(0.73)-\Phi(-1.81)=0.7673-0.0351 = 0.7322$.

Answer:

(a) 0.1977
(b) 0.7322