Q. 6.64 - Elementary Statistics

Question

Determine the area under the standard normal curve that lies between 

a. $-0.88$ and $2.24$.

b. $-2.5$ and $-2$.

c. $1.48$ and $2.72$.

d. $-5.1$ and $1$.

Step-by-Step Solution

Answer

Part $\left(a\right)$: The area under the standard normal curve that lies between $-0.88$ and $2.24$ is, $0.7981$.

Part $\left(b\right)$: The area under the standard normal curve that lies between $-2.5$ and $-2$ is, $0.0166$.

Part $\left(c\right)$: The area under the standard normal curve that lies between $1.48$ and $2.72$ is, $0.0661$.

Part $\left(d\right)$: The area under the standard normal curve that lies between $-5.1$ and $1$ is, $0.8413$.

Part a Step 1 . Given information

We need to find the area for the given values between them.

Part a Step 2 . Let us analyze the give values and find the area for it.

The area under the standard normal curve that lies between $-0.88$ and $2.24$ equals the area to the left of $2.24$ minus the area to the left of $-0.88$.Standard normal table shows that these latter two areas are $0.9875$ and $0.1894$,respectively. So, the required area is, $0.9875-0.1894=0.7981$.

Part a Step 3 . Let us draw a curve which shows the obtained area in it.

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

The area under the standard normal curve that lies between $-2.5$ and $-2$ equals the area to the left of $-2$ minus the area to the left of $-2.5$. Standard normal table shows that these latter two areas are $0.0228$ and $0.0062$. So, the required area is, $0.0228-0.0062=0.0166$.

Part b Step 2 . Le us draw a curve which shows the obtained area on it.

Part c Step 1 . Let us analyze the give values and find the area between them.

The area under the standard normal curve that lies between $1.48$ and $2.72$ equals the area to the left of $2.72$ minus the area to the left of $1.48$.Standard normal table shows that these latter two areas are $0.9967$ and $0.9306$, respectively. So, the required area is. $0.9967-0.9306=0.0661$.

Part c Step 2 . Let us draw a curve which shows the obtained area in it.

Part d Step 1 . Let us analyze the given values and find the area between them.

The area under the standard normal curve that lies between $-5.1$ and $1$ equals the area to the left of $1$ minus the area to the left of $-5.1$. Standard normal table shows that these latter two areas are $0.8413$ and $0.0000$,respectively. So, the required area is, $0.8413-0.0000=0.8413$.

Part d Step 2 . Let us draw a curve which shows the obtained area in it.