Question

find the indicated area under the standard normal curve. to the left of z = - 3.06 and to the right of z = 3.06 click here to view page 1 of the standard normal table. click here to view page 2 of the standard normal table. the total of the area to the left of z = - 3.06 and the area to the right of z = 3.06 under the standard normal curve is . (round to four decimal places as needed)

Explanation:

Step1: Use standard - normal table

The standard - normal table gives the cumulative distribution function $\varPhi(z)$ which is the area to the left of $z$ under the standard - normal curve. Looking up $z = - 3.06$ in the standard - normal table, we find $\varPhi(-3.06)$.

Step2: Find area to the left of $z=-3.06$

From the standard - normal table, $\varPhi(-3.06)=0.0011$.

Step3: Use symmetry of the standard - normal curve

The standard - normal curve is symmetric about $z = 0$. So the area to the right of $z = 3.06$ is the same as the area to the left of $z=-3.06$. That is, $P(Z>3.06)=P(Z < - 3.06)$.

Step4: Calculate the total area

The total area to the left of $z=-3.06$ and to the right of $z = 3.06$ is $P(Z < - 3.06)+P(Z>3.06)=2P(Z < - 3.06)$. Substituting the value of $P(Z < - 3.06)=0.0011$, we get $2\times0.0011 = 0.0022$.

Answer:

$0.0022$