Draw a vertical line through s normal distribution for each of the following z-score locations. Determine whether the tail is on the right or left side of the line and find the proportion in the tail.
a. z=2.00
b. z=0.60
c. z= -1.30
d. z= -0.30
We cannot draw on these posts. The Z score is your score in terms of standard deviations from the mean. There would be a tail on both sides. Are you looking for the smaller portion?
https://www.google.com/search?client=safari&rls=en&q=normal+distribution+standard+deviation&ie=UTF-8&oe=UTF-8
To draw a vertical line through a normal distribution for a given z-score location, we need to understand the standard normal distribution and how to find the proportion in the tail.
The standard normal distribution has a mean of 0 and a standard deviation of 1. It is often represented by the letter "Z". A positive z-score is to the right of the mean, while a negative z-score is to the left of the mean.
To find the proportion in the tail, we can use a z-table, which gives the cumulative probabilities up to a given z-score.
Let's answer each question one by one:
a. z = 2.00
To draw a vertical line for z = 2.00, we can start by drawing a horizontal line representing the mean (0) on the x-axis. Then, we extend the line upwards. The tail will be on the right side of the line. To find the proportion in the tail, we can look up the value in the z-table. From the table, we find that the cumulative probability for z = 2.00 is 0.9772. The proportion in the tail is 1 - 0.9772 = 0.0228.
b. z = 0.60
Following the same procedure, we draw a vertical line for z = 0.60, with the mean at the center. This time, the tail will be on the right side of the line. Using the z-table, we find that the cumulative probability for z = 0.60 is 0.7257. The proportion in the tail is 1 - 0.7257 = 0.2743.
c. z = -1.30
For z = -1.30, we draw a vertical line with the mean as the center. The tail will be on the left side of the line. Using the z-table, we find that the cumulative probability for z = -1.30 is 0.0968. The proportion in the tail is 0.0968.
d. z = -0.30
Lastly, for z = -0.30, we draw a vertical line with the mean as the center. The tail will be on the left side of the line. Using the z-table, we find that the cumulative probability for z = -0.30 is 0.3821. The proportion in the tail is 0.3821.
By following these steps, we can draw the vertical lines through the normal distribution and determine the tail side as well as the proportion in the tail for each given z-score location.