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 P16​, the 16th percentile. This is the bone density score separating the bottom 16% from the top 84%.       Question content area bottom Part 1 Which graph represents P16​? Choose the correct graph below.     A.             x P16         A symmetric bell-shaped curve is plotted over a horizontal x-scale. A vertical line segment runs from the scale to the curve at labeled coordinate P subscript 16, which is to the left of the curve’s center and peak; the segment’s height is approximately 60 percent of the height of the curve at its peak. The area under the curve to the right of the vertical line is shaded.   B.               x P16         A symmetric bell-shaped curve is plotted over a horizontal x-scale. A vertical line segment runs from the scale to the curve at labeled coordinate P subscript 16, which is to the left of the curve’s center and peak; the segment’s height is approximately 60 percent of the height of the curve at its peak. The area under the curve to the left of the vertical line is shaded.   C.             x P16         A symmetric bell-shaped curve is plotted over a horizontal x-scale. A vertical line segment runs from the scale to the curve at labeled coordinate P subscript 16, which is to the right of the curve’s center and peak; the segment’s height is approximately 60 percent of the height of the curve at its peak. The area under the curve to the left of the vertical line is shaded.   D.             x

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 + ...