Question

find the indicated area under the standard normal curve. to the left of z = - 1.63 and to the right of z = 2.41 the total area to the left of z = - 1.63 and to the right of z = 2.41 under the standard normal curve is (round to four decimal places as needed.)

Explanation:

Step1: Find area to the left of z = - 1.63

Use the standard - normal table. The area to the left of $z=-1.63$, denoted as $P(Z < - 1.63)$. Looking up in the standard - normal table, we find $P(Z < - 1.63)=0.0516$.

Step2: Find area to the right of z = 2.41

The area to the right of $z = 2.41$ is $P(Z>2.41)$. Since the total area under the standard - normal curve is 1, and $P(Z>z)=1 - P(Z < z)$. Looking up $P(Z < 2.41)$ in the standard - normal table, we get $P(Z < 2.41)=0.9920$. So $P(Z>2.41)=1 - 0.9920 = 0.0080$.

Step3: Calculate the total area

The total area to the left of $z=-1.63$ and to the right of $z = 2.41$ is the sum of the two areas. Let $A$ be the total area, then $A=P(Z < - 1.63)+P(Z>2.41)$. Substituting the values we found: $A = 0.0516+0.0080=0.0596$.

Answer:

$0.0596$