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$1$.

Short 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,$0.8413$.

Step-by-step solution

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.