Q. 6.6 - Elementary Statistics

Question

Determine the area under the standard normal curve that lies between 

a. $-2.18$ and $1.44$.

b. $-2$ and $-1.5$.

c. $0.59$ and $1.51$.

d. $1.1$ and $4.2$.

Step-by-Step Solution

Answer

Part $\left(a\right)$: The area under the standard normal curve that lies between $-2.18$ and $1.44$ is, $0.9105$.

Part $\left(b\right)$: The area under the standard normal curve that lies between $-2$ and$-1.5$ is, $0.0440$.

Part$\left(c\right)$:The area under the standard normal curve that lies between $0.59$ and $1.51$ is, $0.2121$.

Part$\left(d\right)$:The area under the standard normal curve that lies between $1.1$ and $4.2$ is, $0.1357$.

Part a Step 1 . Given information

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

Part a Step 2 . Let us analyze the given values and find the area between them.

The area under the standard normal curve that lies between $-2.18$ and $1.44$ equals the area to the left of $1.44$ minus the area to the left of $-2.18$. Standard normal table shows that these latter two areas are $0.9251$ and $0.0146$ respectively. So, the required area is, $0.9251-0.0146=0.9105$.

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 between them.

The area under the standard normal curve that lies between $-2$ and $-1.5$ equals the area to the left of $-1.5$ minus the area to the left of $-2$. Standard normal table shows that these latter two areas are $0.0668$ and $0.0228$ respectively. So, the required area is, $0.0668-0.0228=0.0440$.

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

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

The area under the standard normal curve that lies between $0.59$ and $1.51$ equals the area to the left of $1.51$ minus the area to the left of $0.59$.Standard normal table shows that these latter two areas are $0.9345$ and $0.7224$ respectively. So, the required area is, $0.9345-0.7224=0.2121$.

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 $1.1$ and $4.2$ equals the area to the left of $4.2$ minus the area to the left of $1.1$.Standard normal table shows that these latter two areas are $1.0000$ and $0.8643$ respectively. So, the required area is, $1.0000-0.8643=0.1357$.

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