Questions: 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. Draw a graph and find the probability of a bone density test score greater than 0.81. Sketch the region. Choose the correct graph below. A. B. C. D. The probability is . . (Round to four decimal places as needed.)

Solution Steps

The problem states that the bone density test scores are normally distributed with a mean (μ) of 0 and a standard deviation (σ) of 1. We need to find the probability of a bone density test score greater than 0.81.

Since the mean is 0 and the standard deviation is 1, the score of 0.81 is already in standard form (z-score). Therefore, we do not need to standardize it further.

To find the probability of a score greater than 0.81, we look up the z-score of 0.81 in the standard normal distribution table. The table gives the probability of a score being less than 0.81.

The probability of a z-score being less than 0.81 is approximately 0.7910. Therefore, the probability of a z-score being greater than 0.81 is: \[ P(Z > 0.81) = 1 - P(Z < 0.81) = 1 - 0.7910 = 0.2090 \]

The correct graph should show the area to the right of 0.81 shaded. This corresponds to option C.

Final Answer