Q. 6.60 - Elementary Statistics

Question

Determine the area under the standard normal curve that lies to the left of 

a. $-0.87$

b. $3.56$

c. $5.12$

Step-by-Step Solution

Answer

Part $\left(a\right)$: The area under the standard normal curve that lies to the left of $-0.87$ is, $0.1922$.

Part $\left(b\right)$: The area under the standard normal curve that lies to the left of $3.56$ is, $0.9998$.

Part $\left(c\right)$: The area under the standard normal curve that lies to the left of $5.12$ is, $1.000$.

Part a Step 1 . Given information

We need to find the area for the given values.

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

Since $-0.87$ is negative, we use the standard normal table of negative $z$-score. First we go down to the right hand column, labeled $z$ to $-0.8$. Then, going across that row to the column labeled $0.07$, we reach $0.1922$.

Therefore, the area under the standard normal curve that lies to the left of $-0.87$ is, $0.1922$.

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 $3.56$ is positive, we use the standard normal table of positive $z$-score. First, we go down to the left-hand column, labeled $z$ to $3.5$.The, going across that row to the column labeled $0.06$,we reach $0.9998$.

Therefore, the area under the standard normal curve that lies to the left of $3.56$ is, $0.9998$.

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

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

Since $5.12$ is positive, we use the standard normal table of positive $z$-score. But the value of $5.12$ is not available in the table. So, we use the area under the standard normal curve that lies to the left of $5.12$ is, $1.0000$.