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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 \(1 .\) In each case, draw a graph, then find the bone density test score corresponding to the given information. Round results to two decimal places. Find \(P_{99}\), the 99 th percentile. This is the bone density score separating the bottom \(99 \%\) from the top \(1 \%\).

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2. About ________ \(\%\) of the area is between \(z=-2\) and \(z=2\) (or within 2 standard deviations of the mean).

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2. About _______ \(\%\) of the area is between \(z=-3\) and \(z=3\) (or within 3 standard deviations of the mean).

Find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2. About \(\quad \%\) of the area is between \(z=-3.5\) and \(z=3.5\) (or within \(3.5\) standard deviations of the mean).