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=-2 and z=2 (or within 2 standard deviations of the mean). About % of the area is between z=-2 andz=2 (or within 2 standard deviations of the mean). (Round to two decimal places as needed.)

Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. Z = -0.92 z=1.29 The area of the shaded region is (Round to four decimal places as needed.) ☑

The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = *- can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that by the size of each chunk (the standard deviation) you are measuring the distance in units of the size of the standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ+Z.o can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. tells you how far from the mean the data value is (since Z is the number of standard deviations and is the size of each standard deviation the product tells the total distance). So adding the distance from the mean to the mean gives the location along the number line for the data value. A…

For each z score that follows, find the percentage of scores at that value or higher in the normal distribution: + 1.67 -2.02 + 0.08