Question

find the indicated area. find the area under the standard normal curve between z = 0 and z = 3. 0.4987 0.0010 0.9987 0.4641 multiple choice 4 points

Explanation:

Step1: Recall standard - normal table use

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

Step2: Calculate the required area

We want to find the area between $z = 0$ and $z = 3$. We know that $\varPhi(0)=0.5$ (since the standard - normal distribution is symmetric about $z = 0$) and $\varPhi(3)\approx0.9987$ from the standard - normal table. The area $A$ between $z = 0$ and $z = 3$ is given by $A=\varPhi(3)-\varPhi(0)$.
Substituting the values, we get $A = 0.9987-0.5=0.4987$.

Answer:

A. 0.4987