Assume bone density test scores are normally distributed so that the mean is fix

Question

Assume bone density test scores are normally distributed so that the mean is fixed at 0 and the standard deviation at 1. Find the following: a. The cut-off point representing the 99^th percentile, P_99. In other words, find the data value that separates the bottom 99% from the top 1%. b. Find the cut-off point representing the 5^th percentile, P_5. In other words, find the data value that separates the bottom 5% from the top 95%. c. Find the cut-off point representing the 50^th percentile, P_50. In other words, find the data value that separates the bottom 50% from the top 50%.

Explanation / Answer

A. We need to find this value from the normal distribution table . Looking at the value for 0.99 we get z value of 2.33 which is the correct answer

B. For probability of 0.05 we can find the z value for 0.95 and negate it. This means we get -1.65

C. For 0.5 we get the value of 0

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