3. Which graph best shows a shaded area under the curve of a standard normal distribution that represents the percentage of data that falls below the data value associated with a z-score of 0.64?

Graph B

Step-by-step explanation:

Z-score, commonly denoted as , tells us the distance a certain value is from the mean of a data set, in terms of standard deviation.

The ± on a z-score tells us if the value is below or above the mean. A negative z-score indicates the value is below the mean, and a positive score indicates the value is above the meanThe magnitude or absolute value of the z-score tells us exactly how far below or above the mean a score is, in terms of standard deviation. For example, a z-score of -1.5 would indicate that the value is 1.5 standard deviations below the mean.

The z-score given is 0.64. Let's analyze this score:

Since the z-score is positive, the specific value must be above the mean. The magnitude, 0.64, indicates that the value is exactly 0.64 standard deviations above the mean.

We want to find a graph that shades the area under the curve of a standard normal distribution that represents the percentage of data that falls below the data value. Since the x-axis increases as we go right and decreases as we go left, the shading should be on the left side of the specific value. This eliminates answer choices A and C, because there exists no x-value such that everything to the left of it is shaded.

In a normal distribution, the mean is always at the peak, or center, of the graph. Since we know a positive z-score indicates that the value is greater than the mean, the specific value must be to the right of the mean, and everything to the left shaded (the line that separates shaded and non-shaded must to the right of the center in this case). Therefore, we eliminate answer choice D and we get our final answer of graph B.

5/ 1/3=15 i think sorry if im wrong

6xy and -16xy000000000