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=-0.83 z124 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!
![**Finding the Area of the Shaded Region in a Standard Normal Distribution**
*Problem:*
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with a mean of 0 and a standard deviation of 1.
[Image of a Standard Normal Distribution Graph]
The graph shows a bell-shaped curve, representing the standard normal distribution. The shaded region under the curve is between two z-scores: \( z = -0.83 \) and \( z = 1.24 \).
*Instruction:*
The area of the shaded region is to be calculated.
*Answer:*
The area of the shaded region is: \[ \underline{\hspace{2cm}} \]
(Round to four decimal places as needed.)
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**Graph Explanation:**
The graph visually represents the standard normal distribution—a bell-shaped curve symmetrical about the mean. The x-axis denotes z-scores (standardized scores), while the y-axis denotes the probability density.
Key features of the graph:
- **Mean (μ)**: 0 (center of the curve)
- **Standard Deviation (σ)**: 1
- **Shaded Region**: The area under the curve between z = -0.83 and z = 1.24, indicating the probability corresponding to this range of z-scores.
To find the area of the shaded region, which represents the probability between these two z-scores, you should use the standard normal distribution table or a statistical tool.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15c363dd-bee0-4851-8a57-e357b273329c%2Fa51c0106-8063-401e-83d9-9bd928121694%2F4ixjldh_processed.jpeg&w=3840&q=75)
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