Q. 14 - Elementary Statistics

Question

14. Explain how to use Table II to determine the area under the standard normal curve that lies

a. to the left of a specified z-score.

b. to the right of a specified z-score.

c. between two specified z-scores.

Step-by-Step Solution

Answer

a. The first step is to identify the appropriate table. From the table, note the area. 

b. One minus the area acquired from the table equals the area right to the z score.

c. The area is in the middle of two z scores: large area - small area.

Part (a) Step 1: Given Information

Use Table II to determine the area under the standard normal curve that lies to the left of a specified $z-$score.

Part (a) Step 2: Explanation

Suppose you have a $z-$score of $1$and the area under the standardized curve is to the left.

The first step is to identify the table for a particular area. 

The area is directly determined by the table.

Part (b) Step 3: Given Information

To demonstrate how to find the area under the standard normal curve that lies between two

specified $z-$scores using table II.

Part (b) Step 4: Explanation

Imagine the statement, "the area under the standardized curve is equal to the provided $z-$score."

One minus the area acquired from the table equals the area right to the $z-$score.

Part (c) Step 5: Given Information

To demonstrate how to find the area under the standard normal curve that exists between two z- scores using table II.

Part (c) Step 6: Explanation

"Area under the standardized curve lies between two $z-$scores" is an example.

To begin, read the area directly for two $z-$scores and remove them.

$\text{ area lies between two z scores }=\text{ large area }-\text{ small area }$