Area Under Normal Curve: -1.0 to -2.0

D

From the z-tables, z = 1 is 0.3413 and z = 2 is 0.4772. So the area in between is 0.4772 - 0.3413 = 0.1359.

To determine the area under the normal curve between z = -1.0 and z = -2.0, we need to calculate the area under the standard normal distribution curve between these two z-scores.

The standard normal distribution is a symmetric bell-shaped curve with a mean of 0 and a standard deviation of 1. It is often denoted as N(0, 1), where 0 represents the mean and 1 represents the standard deviation.

The area under the normal curve represents the probability of a random variable falling within a specific range. In this case, we want to find the probability of the random variable falling between z = -1.0 and z = -2.0.

To calculate this, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution.

Using a standard normal distribution table or calculator, we can find the area to the left of z = -1.0 and the area to the left of z = -2.0. Then, we subtract the smaller area from the larger area to find the area between the two z-scores.

Looking up the values in a standard normal distribution table, we find:

• The area to the left of z = -1.0 is approximately 0.1587.
• The area to the left of z = -2.0 is approximately 0.0228.

Now, we subtract the smaller area (0.0228) from the larger area (0.1587):

0.1587 - 0.0228 = 0.1359

Therefore, the area under the normal curve between z = -1.0 and z = -2.0 is approximately 0.1359.

The correct answer is D. 0.1359.