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 od 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

To draw a vertical line through a normal distribution for each z-score location, we need to determine whether the body is on the right or left side of the line and find the proportion in the body.

a) For z = 2.20:
The body is on the right side of the line. The proportion in the body can be found using the standard normal table or a calculator. Looking up the z-score in a standard normal table, we find that the proportion to the right of z = 2.20 is approximately 0.0139. Therefore, the proportion in the body to the left of the line is 1 - 0.0139 = 0.9861.

b) For z = 1.60:
The body is on the right side of the line. Using the standard normal table, we find that the proportion to the right of z = 1.60 is approximately 0.0548. Therefore, the proportion in the body to the left of the line is 1 - 0.0548 = 0.9452.

c) For z = -1.50:
The body is on the left side of the line. Using the standard normal table, we find that the proportion to the left of z = -1.50 is approximately 0.0668. Therefore, the proportion in the body to the right of the line is 1 - 0.0668 = 0.9332.

d) For z = -0.70:
The body is on the left side of the line. Using the standard normal table, we find that the proportion to the left of z = -0.70 is approximately 0.2420. Therefore, the proportion in the body to the right of the line is 1 - 0.2420 = 0.7580.

To determine the proportion and left/right side of the normal distribution for each z-score location, we can use a standard normal distribution table or a calculator. However, I will explain how to find the answers using a standard normal distribution table.

Step 1: Understand the standard normal distribution table
A standard normal distribution table provides the cumulative probability up to a specified z-score location, which represents the area under the normal curve. The table gives the proportion of the distribution to the left of the z-score.

Step 2: Locate the z-score location in the table
For each z-score location given, locate the corresponding row and column in the standard normal distribution table. Find the corresponding value in the body of the table. If the exact value is not present, use the closest value and apply rounding if necessary.

a. z = 2.20
In the standard normal distribution table, a z-score of 2.20 falls between 2.1 and 2.2. The closest value in the table is 0.9857. This value represents the proportion to the left of the z-score.

Drawing a vertical line through the normal distribution at z = 2.20 will divide the body of the distribution into two parts. The line will be on the right side of the mean (0) because z = 2.20 is positive. The proportion in the body to the left of the line is approximately 0.9857.

b. z = 1.60
In the standard normal distribution table, a z-score of 1.60 is not present exactly. The closest values are 1.5 and 1.6, with corresponding proportions of 0.9332 and 0.9452 respectively. Since 1.60 is closer to 1.5, we will use 0.9332.

Drawing a vertical line through the normal distribution at z = 1.60 will divide the body of the distribution into two parts. The line will be on the right side of the mean (0) because z = 1.60 is positive. The proportion in the body to the left of the line is approximately 0.9332.

c. z = -1.50
In the standard normal distribution table, a z-score of -1.50 falls between -1.4 and -1.5. The closest value in the table is 0.0668. This value represents the proportion to the left of the z-score.

Drawing a vertical line through the normal distribution at z = -1.50 will divide the body of the distribution into two parts. The line will be on the left side of the mean (0) because z = -1.50 is negative. The proportion in the body to the left of the line is approximately 0.0668.

d. z = -0.70
In the standard normal distribution table, a z-score of -0.70 is not present exactly. The closest values are -0.6 and -0.7, with corresponding proportions of 0.2743 and 0.2420 respectively. Since -0.70 is closer to -0.7, we will use 0.2420.

Drawing a vertical line through the normal distribution at z = -0.70 will divide the body of the distribution into two parts. The line will be on the left side of the mean (0) because z = -0.70 is negative. The proportion in the body to the left of the line is approximately 0.2420.

This is a little clearer. The larger portion (body) for positive Z scores is to the left. For negative Z scores, it is to the right.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability in the larger portion for each Z score.