Find the area of the shaded region under the standard normal curve. E Click here to view the standard normal table Z-0 82 The area of the shaded region is (Round to four decimal places as needed.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![**Find the Area of the Shaded Region Under the Standard Normal Curve**
To find the area of the shaded region under the standard normal curve, please follow these steps:
- **Click Here to View the Standard Normal Table**: Use the link provided to access the standard normal distribution table, which will help you find the area corresponding to a given z-score.
**Diagram Explanation**:
On the right side, there is a graph of the standard normal distribution curve. The curve is bell-shaped and symmetrical.
- **Shaded Region**: The region to the right of the z-score line, where \( z = 0.82 \), is shaded. This indicates the area of interest under the curve.
**Goal**: Calculate the area of the shaded region.
**Instructions**:
1. Use the standard normal table to find the area to the left of \( z = 0.82 \).
2. Subtract this area from 1 to get the area of the shaded region to the right of \( z = 0.82 \).
3. **Round to Four Decimal Places as Needed**: Enter your answer in the box provided.
**The area of the shaded region is**: [ ]
This educational task emphasizes understanding how to use the standard normal table and how to interpret areas under a normal distribution curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76f7a34-206d-42c9-9c55-ed9c63cc7f2d%2F95c46331-cc93-4aa1-8338-7fc560f693d4%2Feyi9kwt_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 7 images
