Draw a vertical line through a normal distribution for each of the following z- score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. (a). z = 2.20 (b) z = 1.60

(c) z = -1.50 (d) z = - 0.70

What do you mean by "the body?"

To draw a vertical line through a normal distribution for each of the given z-score locations, follow these steps:

Step 1: Start with a normal distribution curve. This is a bell-shaped curve that represents a standard normal distribution.

Step 2: Identify the mean (μ) and standard deviation (σ) of the distribution. The mean represents the center of the curve, and the standard deviation determines the spread or width of the curve.

Step 3: For each z-score, calculate the corresponding value using the formula: x = μ + (z * σ). This formula will convert the z-scores to actual values on the x-axis.

Step 4: Draw a vertical line through the calculated x-value on the normal distribution curve. The line should go through the point representing the x-value.

Step 5: Determine whether the body (area) of the normal distribution curve is on the right or left side of the line. If the z-score is positive, the body will be on the right side of the line. If the z-score is negative, the body will be on the left side of the line.

Step 6: Calculate the proportion in the body of the normal distribution curve. This represents the area under the curve on the specified side of the line. You can use a standard normal distribution table or a statistical software to find the proportion.

Now let's apply these steps to each given z-score:

(a) z = 2.20:
- Calculate x: x = μ + (z * σ)
- Draw a vertical line through the calculated x-value on the normal distribution curve.
- The body is on the right side of the line because the z-score is positive.
- Calculate the proportion in the body using a standard normal distribution table or software.

(b) z = 1.60:
- Calculate x: x = μ + (z * σ)
- Draw a vertical line through the calculated x-value on the normal distribution curve.
- The body is on the right side of the line because the z-score is positive.
- Calculate the proportion in the body using a standard normal distribution table or software.

(c) z = -1.50:
- Calculate x: x = μ + (z * σ)
- Draw a vertical line through the calculated x-value on the normal distribution curve.
- The body is on the left side of the line because the z-score is negative.
- Calculate the proportion in the body using a standard normal distribution table or software.

(d) z = -0.70:
- Calculate x: x = μ + (z * σ)
- Draw a vertical line through the calculated x-value on the normal distribution curve.
- The body is on the left side of the line because the z-score is negative.
- Calculate the proportion in the body using a standard normal distribution table or software.

By following these steps, you can draw a vertical line through a normal distribution for each given z-score location, determine whether the body is on the right or left side of the line, and find the proportion in the body.