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$4.2$.

Short 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,$0.1357$.

Step-by-step solution

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.