Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. z= -0.91 z=121 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!
Key points from the graph:
- **z = -0.91**
- **z = 1.21**
The shaded region of the graph represents the area under the standard normal distribution curve between the z-scores of -0.91 and 1.21.
**Calculation of Area:**
\[ \text{The area of the shaded region is } \text{[______]} \]
*Note: Round your answer to four decimal places as needed.*
### Understanding the Graph
The graph demonstrates a standard normal distribution, which is a bell-shaped curve centered at 0 with a spread determined by the standard deviation of 1. The shaded area is the probability that a value falls between the two z-scores, -0.91 and 1.21. Calculating this area typically involves using z-tables or statistical software to find precise values.
For educational purposes, students should familiarize themselves with tools like z-tables or computational software to accurately determine these areas as part of their statistical learning outcomes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F433a8f27-8930-42f3-908d-a0ccaa45c243%2Fa5a67aa7-7080-4fd8-aeb7-da0bd0c90a7b%2Ftg9g4xk.jpeg&w=3840&q=75)
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