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 15​% and highest 15​%, indicating levels that are too low or too​ high, respectively.       Sketch the region. Choose the correct graph below.     A.                      −zα zα         A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical line segments run from the horizontal axis to the curve. One vertical line is at the labeled coordinate negative z Subscript alpha, which is to the left of the curve's center and peak. The other vertical line is at the labeled coordinate z Subscript alpha, which is to the right of the curve's center and peak. The areas under the curve to the left of negative z Subscript alpha and to the right of z Subscript alpha are shaded. Your answer is correct.   B.                    −zα zα         A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical line segments run from the horizontal axis to the curve. One vertical line is at the labeled coordinate negative z Subscript alpha, which is to the left of the curve's center and peak. The other vertical line is at the labeled coordinate z Subscript alpha, which is to the right of the curve's center and peak. The area under the curve between negative z Subscript alpha and z Subscript alpha is shaded.   C.                   −zα zα         A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical line segments run from the horizontal axis to the curve. One vertical line is at the labeled coordinate negative z Subscript alpha, which is to the left of the curve's center and peak. The other vertical line is at the labeled coordinate z Subscript alpha, which is to the right of the curve's center and peak. The area under the curve to the right of negative z Subscript alpha is shaded.   D.                      −zα zα         A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical line segments run from the horizontal axis to the curve. One vertical line is at the labeled coordinate negative z Subscript alpha, which is to the left of the curve's center and peak. The other vertical line is at the labeled coordinate z Subscript alpha, which is to the right of the curve's center and peak. The area under the curve to the left of z Subscript alpha is shaded. The bone density scores are

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...