Consider the standard normal distribution. Find the area for the z-score -0.75. Draw a picture of this distribution showing the location of the z-score and the mean. Shade the region corresponding to the area found for the z-score.
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To find the area corresponding to a particular z-score in a standard normal distribution, you can use a Z-table or a statistical software. The Z-table provides you with the probability (area) associated with each z-score.
Here's how you can find the area for a z-score of -0.75 using a Z-table:
1. Start by accessing a Z-table, which can be found in statistics textbooks or online.
2. Locate the row that corresponds to the tenths digit of the z-score (-0.7) and the column that corresponds to the hundredths digit of the z-score (0.05).
3. The value in the intersection of the row and column represents the area to the left of the z-score. In this case, the value is 0.2266.
4. However, since we want the area to the right (or above) the z-score, we subtract the value obtained in the previous step from 1. In this case, 1 - 0.2266 = 0.7734.
The area corresponding to a z-score of -0.75 is approximately 0.7734.
Now, let's draw a picture of the standard normal distribution to visualize the location of the z-score and the calculated area:
1. Begin by drawing a horizontal number line labeled with z-scores. Place the mean (0) at the center of the line.
2. On the left side of the mean, mark the z-score -0.75. This point will be located to the left of the mean.
3. Shade the region to the right of the z-score (-0.75) to represent the area calculated earlier (approximately 0.7734). This shaded region will extend from the z-score to the end of the number line.
By following these steps, you will have a visual representation of the standard normal distribution with the z-score -0.75 and the shaded region representing the area found.
To find the area for the z-score -0.75 in the standard normal distribution, you can use a standard normal distribution table or a calculator.
Step 1: Locate the z-score -0.75 on the standard normal distribution.
The z-score represents the number of standard deviations a value is from the mean. In this case, the z-score is -0.75. To locate this on the standard normal distribution, look for -0.75 on the horizontal axis.
Step 2: Find the area corresponding to the z-score.
Using a standard normal distribution table or a calculator, find the area to the left of -0.75. This area represents the cumulative probability up to the z-score -0.75.
Using a standard normal distribution table, you can find that the area to the left of -0.75 is approximately 0.2266.
Step 3: Draw a picture of the standard normal distribution and shade the region.
Draw a horizontal line representing the standard normal distribution with the mean at the center (z = 0). Locate the z-score -0.75 on the horizontal axis. Shade the region to the left of -0.75.
The shaded region represents the area found for the z-score -0.75.
Remember, the standard normal distribution is symmetrical, so you can also think of the shaded region as the area to the right of 0.75.
I hope this helps! Let me know if you have any other questions.