use this table or the aleks calculator to complete the following. give your answers to four decimal places…

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