Math Problem Statement

Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability of a bone density test score greater than -1.88 and select the correct graph.

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:

  1. The normal distribution curve is symmetric around 0, with most of the area concentrated around the mean.
  2. 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:

  1. How do you calculate probabilities using a Z-score table?
  2. What is the probability of getting a value less than -1.88 in this distribution?
  3. How do we find the area under a normal curve using a calculator?
  4. What does a Z-score represent in a normal distribution?
  5. 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