Q. 6.61 - Elementary Statistics

Question

Find the area under the standard normal curve that lies to the right of 

a. $-1.07$

b. $0.6$

c. $0$

d. $4.2$

Step-by-Step Solution

Answer

Part $\left(a\right)$: The area under the  standard normal curve that lies to the right of $-1.07$ is, $0.8577$.

Part $\left(b\right)$: The area under the standard normal curve that lies to the right of $0.6$ is, $0.2743$.

Part $\left(c\right)$: The area under the standard normal curve that lies to the right of $0$ is, $0.5000$.

Part $\left(d\right)$: The area under the standard normal curve that lies to the right of $4.2$ is, $0.0000$.

Part a Step 1 . Given information

We need to find the area under the standard normal curve that lies to the right for the given values.

Part a Step 2 . Let us analyze the given value and find the area for it.

Since $-1.07$ is negative, we use the standard normal curve of negative $z$ scores. First, we go down to the right-hand column, labeled $z$ to $-1.0$. Then going across that row to the column labeled $0.07$, we reach $0.1423$, which the area under the standard normal curve that lies to the left of $-1.07$.

Therefore, the area under the standard normal curve that lies to the right of $-1.07$ is, $1-0.1423=0.8577$.

Part a Step 3 . Let us draw a curve for the obtained area.

Part b Step 1 . Let us analyze the given value and find the area for it.

Since $0.6$ is positive, we use the standard normal table of positive $z$ scores. First, we go down to the left-hand column, labeled $z$ to $0.6$. Then going across that row to the column labeled $0.00$, we reach $0.7257$, which the area under the standard normal curve that lies to the left of $0.6$.

The area under the standard normal curve that lies to the right of $0.6$ is, $1-0.7257=0.2743$.

Part b Step 2 . Let us draw a curve for the obtained area.

Part c Step 1 . Let us analyze the give value and find the area for it.

We use the standard normal table to find the area for the given value. First, go down to the left hand-column, labeled $z$ to $0.00$. Then going across that row to the column labeled $0.00$, we reach $0.5000$, which is the area under the standard normal curve that lies to the left of $0.00$ is, $0.5000$.

Therefore, the area under the standard normal curve that lies to the right of $0$ is, $1-0.5000=0.5000$.

Part c Step 2 . Let us draw a curve for the obtained area.

Part d Step 1 . Let us analyze the given value and find the area for it.

The value $4.2$ is not in the table. So, we use the area under the standard normal curve that lies to the left of $4.2$ as $1.0000$,which the area under the standard normal curve that lies to the left of $4.2$.

Therefore, the area under the standard normal curve that lies to the right of $4.2$ is, $1-1.0000=0.0000$.