Question

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 between −2.09 and 2.09.

Answer 1

To find the probability of a bone density test score between -2.09 and 2.09, we need to calculate the area under the normal distribution curve for that range.

Step-by-step explanation:

To find the probability of a bone density test score between -2.09 and 2.09, we need to calculate the area under the normal distribution curve for that range. Since the bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1, we can use the standard normal distribution to find the probability.

To do this, we need to find the z-scores for -2.09 and 2.09. The z-score formula is given by z = (x - mean) / standard deviation.

For -2.09:

z = (-2.09 - 0) / 1 = -2.09

For 2.09:

z = (2.09 - 0) / 1 = 2.09

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores. The probability of a bone density test score between -2.09 and 2.09 is the difference between the probabilities corresponding to these z-scores.