Question

statistics computing standard normal probabilities 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 = 1.03. (b) find the area under the standard normal curve between z = - 1.96 and z = 2.22.

Explanation:

Step1: Recall standard - normal property for (a)

The total area under the standard - normal curve is 1. The area to the left of $z = 1.03$ is $\Phi(1.03)$. The area to the right of $z = 1.03$ is $1-\Phi(1.03)$. Using a standard - normal table or calculator, $\Phi(1.03)=0.8485$, so the area to the right is $1 - 0.8485=0.1515$.

Step2: Recall standard - normal property for (b)

The area under the standard - normal curve between $z=-1.96$ and $z = 2.22$ is $\Phi(2.22)-\Phi(-1.96)$. Since $\Phi(-z)=1 - \Phi(z)$, then $\Phi(-1.96)=1-\Phi(1.96)$. Using a standard - normal table or calculator, $\Phi(2.22)=0.9868$ and $\Phi(1.96)=0.9750$, so $\Phi(-1.96)=1 - 0.9750 = 0.0250$. Then the area between $z=-1.96$ and $z = 2.22$ is $0.9868-0.0250 = 0.9618$.

Answer:

(a) 0.1515
(b) 0.9618