Q.6.57 - Elementary Statistics

Question

Explain how Table II is used 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). Straight from the table.

b). Area to the right $=1-$Area given.

c). Area between two $z$-scores $=$ Larger given area - Smaller given area.

Part (a) Step 1: Given Information

The left of a specified $z$-score.

Part (a) Step 2: Explanation

Directly reading the area under the normal curve to the left of the supplied $z$-score yields the area under the normal curve to the left of the specified $z$-score.

Part (b) Step 1: Given Information

The procedure for calculating the area under the curve to the right of a given $z$-score.

Part (b) Step 2: Explanation

By directly reading the area from the table and subtracting it from $1$, you may get the area under the normal curve to the right of the supplied $z$-score.

Area to the right $=1 -$ Area to the left

Area to the right $=1-$ Area given

Part (c) Step 1: Given Information

The area beneath the curve between two $z$- scores.

Part (c) Step 2: Explanation

By subtracting the smaller area from the larger area, the area under the normal curve between two specified z-scores can be obtained.

The area between two $z$-scores $=$ Larger given area - Smaller given area.