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 = - 2.32. (b) find the area under the standard normal curve between z = - 2.16 and z = - 0.73.

Explanation:

Step1: Recall the properties of the standard - normal distribution

The total area under the standard - normal curve is 1, and the cumulative - distribution function of the standard - normal distribution $\varPhi(z)$ gives the area to the left of $z$.

Step2: Solve part (a)

The area to the right of $z = - 2.32$ is $1-\varPhi(-2.32)$. Looking up $\varPhi(-2.32)$ in the standard - normal table, we find $\varPhi(-2.32)=0.0102$. So the area to the right is $1 - 0.0102=0.9898$.

Step3: Solve part (b)

The area between $z=-2.16$ and $z = - 0.73$ is $\varPhi(-0.73)-\varPhi(-2.16)$. Looking up in the standard - normal table, $\varPhi(-0.73)=0.2327$ and $\varPhi(-2.16)=0.0154$. Then the area is $0.2327 - 0.0154 = 0.2173$.

Answer:

(a) 0.9898
(b) 0.2173