find the area between z=0 and z=0.9 under the standard normal curve is
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability between the two Z scores.
Why did the statistician go to the circus?
Because he wanted to find the area under the Big Top!
But in all seriousness, to find the area between z=0 and z=0.9 under the standard normal curve, you can use a table of z-scores or a statistical software. The area under the curve represents the probability, so you're looking for the probability that a random variable falls between z=0 and z=0.9.
To find the area between z = 0 and z = 0.9 under the standard normal curve, we need to calculate the cumulative probability at each z-value and then subtract the lower value from the higher value.
The cumulative distribution function (CDF) for the standard normal distribution gives the probability of observing a value less than or equal to a given z-score.
Using a statistical software, a calculator, or a z-table, we can find the cumulative probabilities for z = 0 and z = 0.9.
For z = 0, the cumulative probability is: P(Z ≤ 0) = 0.5000
For z = 0.9, the cumulative probability is: P(Z ≤ 0.9) = 0.8159
To find the area between z = 0 and z = 0.9, we subtract the lower probability from the higher probability:
Area = P(Z ≤ 0.9) - P(Z ≤ 0)
= 0.8159 - 0.5000
= 0.3159
Therefore, the area between z = 0 and z = 0.9 under the standard normal curve is approximately 0.3159.
To find the area between z=0 and z=0.9 under the standard normal curve, we can use a standard normal distribution table or a statistical software.
1. Using a Standard Normal Distribution Table:
- Look up the values for z=0 and z=0.9 in the standard normal distribution table.
- The table will provide the corresponding areas under the curve for these z-values.
- Subtract the area corresponding to z=0 from the area corresponding to z=0.9 to find the area between these two values.
2. Using Statistical Software:
- If you have access to statistical software like Excel, R, or Python, you can use their functions to find the area between z=0 and z=0.9.
- For example, in Excel, you can use the NORM.DIST function and specify the lower and upper z-values as arguments to get the area between them.
Both methods will give you the same result, which is the area between z=0 and z=0.9 under the standard normal curve.