Question

1. 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 that a given score is less than 3.87 and draw a sketch of the region.

2. Assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. Draw a graph and find Upper P6​, the 6th percentile. This is the bone density score separating the bottom 6% from the top 94%.

3. 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 bone density test scores that can be used as cutoff values separating the lowest 5​% and highest 5​%, indicating levels that are too low or too​ high, respectively.

4. Find the indicated area under the curve of the standard normal​ distribution; then convert it to a percentage and fill in the blank.

About​ ______% of the area is between z=−3.5 and z=3.5 (or within 3.5 standard deviations of the​ mean).

Answer 1

1. As mean is 0 and S.D=1, it is a standard Normal Z.

2.

3.

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