Q. 6.6 - Elementary Statistics

Question

Use Table II to obtain the areas under the standard normal curve required in Exercises 6.59-6.66. Sketch a standard normal curve and shade the area of interest in each problem.

6.60 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

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

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

c. The area under the standard normal curve that lies to the left of $5.12$ is $1.0000$

Part (a) Step 1: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of $-0.87$

Part (a) Step 2: Explanation

Because the given quantity $-0.87$is negative, the conventional normal table of negative $z$ scores is applied. To begin, travel down the right-hand column called $\text{'}Z\text{'}$ to $-0.8$ and then across the row to the column labeled $\text{'}0.07\text{'}$ to get $0.1922.$

As a result, the region beneath the standard normal to the left of $-0.87$ is $0.1922$.

Part (b) Step 3: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of $3.56$

Part (b) Step 4: Explanation

Because the given number $3.56$ is positive, the typical normal table of positive $z$ scores is employed.

To begin, proceed down the left hand column labeled' $z$ to $3.5$ and then across the row to the column labeled' $0.06$ to get $0.9998$.

As a result, the region beneath the ordinary normal to the left of $3.56$ is $0.9998$.

Part (c) Step 5: Given Information

Use Table II to obtain the areas under the standard normal curve.

Determine the area under the standard normal curve that lies to the left of $5.12$

Part (c) Step 6: Explanation

Because the given quantity $5.12$ is positive, the typical normal table of positive $z$ scores is employed. To begin, travel down the left hand column labeled' $\text{'}z\text{'}$ to $5.1$ and then across the row to the column labeled $0.02$ to get $1.0000$

As a result, the area beneath the usual normal to the left of $5.12$ is $1.0000$.