What is the area under the standard normal distribution curve between z = 1.50 and z = 2.50?

Solution:

The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.

Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.

When you standardize a normal distribution, the mean becomes 0 and the standard deviation becomes 1. A z-score is a standard score that tells you how many standard deviations away from the mean an individual value (x) lies:

• A positive z-score means that your x-value is greater than the mean.
• A negative z-score means that your x-value is less than the mean.
• A z-score of zero means that your x-value is equal to the mean.

From the table,

The area up to z value 2.50 is 0.9938

The area up to z value 1.50 is 0.9332

Now, the area between z value 1.50 and 2.50 = 0.9938 - 0.9332

= 0.0606

Therefore, the area between z value 1.50 and 2.50 is 0.0606

What is the area under the standard normal distribution curve between z = 1.50 and z = 2.50?

Summary:

The area under the standard normal distribution curve between z = 1.50 and z = 2.50 is 0.0606