find the area that corresponds to each of the following z - values. with complete steps.\n1. find the area…

Explanation:

Step1: Recall the standard - normal table

The standard - normal table gives the cumulative distribution function (CDF) of the standard normal distribution $\varPhi(z)$, which is the area to the left of $z$ under the standard - normal curve $N(0,1)$.

Step2: Solve for $z = 1.92$

We look up the value of $z = 1.92$ in the standard - normal table. The area to the left of $z = 1.92$, denoted as $P(Z<1.92)$, from the standard - normal table is $\varPhi(1.92)=0.9726$.

Step3: Solve for $z = 1$

We look up the value of $z = 1$ in the standard - normal table. The area to the left of $z = 1$, denoted as $P(Z < 1)$, from the standard - normal table is $\varPhi(1)=0.8413$.

Step4: Solve for $z = 2$

We know that the total area under the standard - normal curve is 1. The area to the left of $z = 2$ is $\varPhi(2)=0.9772$ from the standard - normal table. The area to the right of $z = 2$ is $P(Z>2)=1 - P(Z < 2)=1 - 0.9772 = 0.0228$.

Answer:

1. The area to the left of $z = 1.92$ is $0.9726$.
2. The area less than $z = 1$ is $0.8413$.
3. The area greater than $z = 2$ is $0.0228$.