3. Find the area under the standard normal curve between z = 0 and z = 1.45.
Draw the graph and find the area under the normal distribution curve which lies from
Well, to find the area under the standard normal curve between z = 0 and z = 1.45, we can use integration methods...or we can just have a dance-off between the z-scores!
Now, picture z = 0 as your typical party pooper who just stands in one spot, doing nothing exciting. Meanwhile, z = 1.45 is the life of the party, busting out some crazy moves, getting everyone's attention!
So, the area under the curve between z = 0 and z = 1.45 represents the space taken up by the party animal z = 1.45, who's stealing the spotlight. And honestly, I don't think anyone would mind that!
Now, let me grab my dancing shoes and disco ball, and let's get this area under the curve party started! *cue funky music*
To find the area under the standard normal curve between z = 0 and z = 1.45, we can use a standard normal distribution table or calculate it using a statistical software or programming language.
Using a standard normal distribution table:
1. Look up the value of 1.45 in the standard normal distribution table. The table will give you the area to the left of 1.45, which represents the area under the curve up to z = 1.45.
2. Look up the value of 0 in the standard normal distribution table. This will give you the area to the left of 0, which represents the area under the curve up to z = 0.
3. Subtract the second value from the first value to find the area under the curve between z = 0 and z = 1.45.
Using statistical software or programming language:
If you have access to a statistical software (e.g., R, Python with scipy library, etc.) or a programming language that has statistical functions, you can use the cumulative distribution function (CDF) of the standard normal distribution to find the area under the curve directly. Here's an example using Python:
```python
import scipy.stats as stats
area = stats.norm.cdf(1.45) - stats.norm.cdf(0)
print("The area under the standard normal curve between z = 0 and z = 1.45 is:", area)
```
The output will give you the area under the curve between z = 0 and z = 1.45.