Percentage of scores falling between a z-score of .54 and the mean.
I can do the math, I just don't understand how to begin!
Thank you.
To find the percentage of scores falling between a z-score of .54 and the mean, you can use the standard normal distribution table or a statistical calculator. Here are the general steps to calculate it:
1. Look up the given z-scores in the standard normal distribution table.
2. Identify the corresponding area under the curve for each z-score. This represents the percentage of scores falling to the left of each z-score.
3. Subtract the smaller area from the larger area to find the percentage of scores falling between the two z-scores.
Let's break it down step-by-step:
Step 1: Look up the z-scores in the standard normal distribution table. The z-score .54 corresponds to an area of 0.7054.
Step 2: Calculate the area to the left of the mean. Since the z-score of the mean is 0, the area to the left of the mean is 0.5.
Step 3: Subtract the smaller area from the larger area. In this case, we subtract 0.5 from 0.7054:
0.7054 - 0.5 = 0.2054
Step 4: Convert the resulting decimal into a percentage by multiplying by 100:
0.2054 x 100 = 20.54%
Therefore, the percentage of scores falling between a z-score of .54 and the mean is approximately 20.54%.
To find the percentage of scores falling between a z-score of 0.54 and the mean, you can use a standard normal distribution table or a calculator that has a built-in normal distribution function. Here's how to do it step by step:
1. Understand the concept: A z-score represents the number of standard deviations a data point is away from the mean in a normal distribution. A positive z-score indicates a data point is above the mean, while a negative z-score indicates a data point is below the mean.
2. Identify the area: Since you want to find the percentage of scores falling between a z-score of 0.54 and the mean, you need to find the area under the curve between the two z-scores. In other words, you want to find the area between 0 (the mean) and 0.54.
3. Use a standard normal table: Look for a standard normal distribution table that provides the areas under the curve for different z-scores. These tables usually have positive z-scores listed, so you might need to use the symmetry property of the normal distribution.
- Find the area for 0.54: Locate the z-score of 0.5 (closest value to 0.54) in the table. Since most tables only provide values up to two decimal places, look for the intersection closest to 0.50 and 0.04. The corresponding area would be 0.7054.
- Find the area for 0 (the mean): The area for a z-score of 0 is always 0.50.
4. Calculate the percentage: Subtract the area for 0 from the area for 0.54 to find the area between them: 0.7054 - 0.50 = 0.2054. Finally, multiply this result by 100 to get the percentage: 0.2054 x 100 ≈ 20.54%.
Therefore, approximately 20.54% of scores fall between a z-score of 0.54 and the mean in a standard normal distribution.
No math, just use the table.
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between the mean and a Z score of .54.