find the area under the normal curve that lies between z=0 and z=2.35?
find the area under the normal curve that lies between z=2.42 and z=1.31?
find the area under the normal curve that lies between z=1.54 and z=2.24?
This will be your friend for these kind of problems
www.davidmlane.com/normal.html
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click on "between" and enter 0 and 2.35 in the boxes shown
you should see 0.4906
do the others.
Why did the normal curve go to therapy?
Because it had Z-score issues!
Now, let's calculate those areas for you:
1. The area under the normal curve between z=0 and z=2.35 is approximately 0.4907.
2. The area under the normal curve between z=2.42 and z=1.31 is approximately 0.0811.
3. The area under the normal curve between z=1.54 and z=2.24 is approximately 0.1190.
Remember, these values are approximate and may vary depending on the method used for calculation.
To find the area under the normal curve between two z-scores, you will need to use the z-table or a calculator with built-in functionality for finding areas under the normal curve.
1. Area between z=0 and z=2.35:
Using the z-table or a calculator, find the area to the left of z=2.35 and subtract the area to the left of z=0. The z-table will give you the area to the left of a given z-score.
Area = P(0 ≤ Z ≤ 2.35) = P(Z ≤ 2.35) - P(Z ≤ 0)
2. Area between z=2.42 and z=1.31:
Again, use the z-table or calculator to find the area to the left of z=2.42 and subtract the area to the left of z=1.31.
Area = P(1.31 ≤ Z ≤ 2.42) = P(Z ≤ 2.42) - P(Z ≤ 1.31)
3. Area between z=1.54 and z=2.24:
Use the same process as above, finding the area to the left of z=2.24 and subtracting the area to the left of z=1.54.
Area = P(1.54 ≤ Z ≤ 2.24) = P(Z ≤ 2.24) - P(Z ≤ 1.54)
To find the area under the normal curve between two z-scores, you can use a standard normal distribution table or a calculator. Here's how you can do it:
1. Using a Standard Normal Distribution Table:
- Look up the z-score for the left boundary of the area (in this case, z=0, z=2.42, and z=1.54) in the table. The table gives you the area to the left of the z-score.
- Look up the z-score for the right boundary of the area (in this case, z=2.35, z=1.31, and z=2.24) in the table.
- Subtract the area to the left of the left boundary from the area to the left of the right boundary to find the area between the two z-scores.
2. Using a Calculator:
- Use a statistical calculator or a normal distribution calculator online.
- Enter the mean (μ) and standard deviation (σ) for the normal distribution. If not given, assume a standard normal distribution with mean=0 and standard deviation=1.
- Enter the left and right z-scores (0 and 2.35, 2.42 and 1.31, or 1.54 and 2.24) to calculate the area between them.
Let's calculate the areas for each of your examples:
1. Area between z=0 and z=2.35:
- Using the standard normal distribution table, we find that the area to the left of z=0 is 0.5000, and the area to the left of z=2.35 is 0.9904.
- Subtracting the two areas (0.9904 - 0.5000), we find that the area between z=0 and z=2.35 is 0.4904.
2. Area between z=2.42 and z=1.31:
- Using the standard normal distribution table, we find that the area to the left of z=2.42 is 0.9929, and the area to the left of z=1.31 is 0.9049.
- Subtracting the two areas (0.9929 - 0.9049), we find that the area between z=2.42 and z=1.31 is 0.0880.
3. Area between z=1.54 and z=2.24:
- Using the standard normal distribution table, we find that the area to the left of z=1.54 is 0.9382, and the area to the left of z=2.24 is 0.9875.
- Subtracting the two areas (0.9875 - 0.9382), we find that the area between z=1.54 and z=2.24 is 0.0493.
Remember to use either a standard normal distribution table or a calculator to find the areas between z-scores on a normal curve accurately.