Math Problem Statement
Solution
The problem asks for the probability of obtaining a bone density test score greater than -1.88, given that the test scores are normally distributed with a mean of 0 and a standard deviation of 1.
We need to find the area to the right of -1.88 under the normal distribution curve. Here's the analysis:
- The normal distribution curve is symmetric around 0, with most of the area concentrated around the mean.
- The probability of getting a score greater than -1.88 corresponds to the area to the right of -1.88.
Looking at the options in the image:
- Option B shows the correct shaded region, which represents the area to the right of -1.88 on a normal distribution curve.
Conclusion:
The correct graph is Option B, which represents the area to the right of -1.88.
Would you like a detailed calculation of this probability? Or any further clarifications?
Here are 5 related questions you might find helpful:
- How do you calculate probabilities using a Z-score table?
- What is the probability of getting a value less than -1.88 in this distribution?
- How do we find the area under a normal curve using a calculator?
- What does a Z-score represent in a normal distribution?
- How would the graph look if we wanted the probability less than 1.88?
Tip: The total area under a normal curve is always 1, representing 100% probability.
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Probability
Z-scores
Formulas
P(Z > -1.88)
Theorems
Empirical Rule
Properties of the Normal Distribution
Suitable Grade Level
Grades 10-12
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