Find the area under the normal distribution curve between z = 0 and z = 3.20.
To find the area under the normal distribution curve between z = 0 and z = 3.20, you can use a standard normal distribution table or a statistical calculator.
If you have access to a standard normal distribution table, you can look up the cumulative probability for z = 0 and z = 3.20 separately and then subtract the smaller value from the larger one to obtain the area between the two z-scores. Here's how:
1. Look up the cumulative probability for z = 0 in the table. The cumulative probability for z = 0 is 0.5000 (this represents half of the area under the curve).
2. Look up the cumulative probability for z = 3.20 in the table. The cumulative probability for z = 3.20 is 0.9993.
3. Subtract the cumulative probability for z = 0 from the cumulative probability for z = 3.20: 0.9993 - 0.5000 = 0.4993.
So, the area under the normal distribution curve between z = 0 and z = 3.20 is approximately 0.4993.
If you prefer to use a statistical calculator, you can use software like R, Python, or Excel. Each of these tools has built-in functions, such as `pnorm` in R or `norm.dist` in Excel, that allow you to calculate the cumulative probability directly and find the area under the curve between two z-scores.