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

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 = - 1.06. (b) find the area under the standard normal curve between z = 1.28 and z = 2.74.

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 = - 1.06. (b) find the area under the standard normal curve between z = 1.28 and z = 2.74.

Answer

Explanation:

Step1: Recall standard - normal table property

The total area under the standard - normal curve is 1. The area to the left of a z - value, denoted as $\varPhi(z)$, can be found from the standard - normal table.

Step2: Find area for part (a)

The area to the left of $z=- 1.06$ is $\varPhi(-1.06)$. From the standard - normal table, $\varPhi(-1.06)=0.1446$. The area to the right of $z =-1.06$ is $1-\varPhi(-1.06)$. So, $1 - 0.1446=0.8554$.

Step3: Find area for part (b)

The area to the left of $z = 1.28$ is $\varPhi(1.28)=0.8997$ and the area to the left of $z = 2.74$ is $\varPhi(2.74)=0.9969$. The area between $z = 1.28$ and $z = 2.74$ is $\varPhi(2.74)-\varPhi(1.28)$. So, $0.9969 - 0.8997=0.0972$.

Answer:

(a) 0.8554 (b) 0.0972